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Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
Book Synopsis Finite Dimensional Algebras and Related Topics by : V. Dlab
Download or read book Finite Dimensional Algebras and Related Topics written by V. Dlab and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Book Synopsis Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by : Vlastimil Dlab
Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on 2004 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Book Synopsis Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by : Vlastimil Dlab
Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.
Book Synopsis Finite Dimensional Algebras by : Yurj A. Drozd
Download or read book Finite Dimensional Algebras written by Yurj A. Drozd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.
This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Book Synopsis Trends in Representation Theory of Algebras and Related Topics by : Andrzej Skowroński
Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
$\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.
Book Synopsis $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations by : Nathanial Patrick Brown
Download or read book $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations written by Nathanial Patrick Brown and published by American Mathematical Soc.. This book was released on 2008 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: $\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.
This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.
Book Synopsis Representations of Algebras and Related Topics by : Andrzej Skowroński
Download or read book Representations of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2011 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.
This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13-18, 1990. The conference focused on the rapid development of research on representations of finite-dimensional algebras and group representations. A subset of the fifty-seven lectures are collected here, together with a number of other papers not originally presented at the conference. With contributions by some of the world's leading experts in this area, this book provides a valuable overview of the frontier of research in representations of algebras.
Book Synopsis Representations of Finite Dimensional Algebras by : Hiroyuki Tachikawa
Download or read book Representations of Finite Dimensional Algebras written by Hiroyuki Tachikawa and published by American Mathematical Soc.. This book was released on 1991 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13-18, 1990. The conference focused on the rapid development of research on representations of finite-dimensional algebras and group representations. A subset of the fifty-seven lectures are collected here, together with a number of other papers not originally presented at the conference. With contributions by some of the world's leading experts in this area, this book provides a valuable overview of the frontier of research in representations of algebras.
This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.
Book Synopsis Representations of Algebras and Related Topics by : Ragnar-Olaf Buchweitz
Download or read book Representations of Algebras and Related Topics written by Ragnar-Olaf Buchweitz and published by American Mathematical Soc.. This book was released on with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.
Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Algebras and Modules I by : Idun Reiten
Download or read book Algebras and Modules I written by Idun Reiten and published by American Mathematical Soc.. This book was released on 1998 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
