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This book presents an analysis of a variety of central linguistic notions, such as case agreement, obviation, and rigidity, from a derivational perspective.
Book Synopsis Derivations by : Juan Uriagereka
Download or read book Derivations written by Juan Uriagereka and published by Routledge. This book was released on 2005-08-11 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an analysis of a variety of central linguistic notions, such as case agreement, obviation, and rigidity, from a derivational perspective.
A pathbreaking new perspective on derivation, the series of operations by which sentences are formed.
Book Synopsis Derivations in Minimalism by : Samuel David Epstein
Download or read book Derivations in Minimalism written by Samuel David Epstein and published by Cambridge University Press. This book was released on 2006-01-20 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pathbreaking new perspective on derivation, the series of operations by which sentences are formed.
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Book Synopsis Algebraic Theory of Locally Nilpotent Derivations by : Gene Freudenburg
Download or read book Algebraic Theory of Locally Nilpotent Derivations written by Gene Freudenburg and published by Springer. This book was released on 2017-09-08 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Book Synopsis Automorphisms and Derivations of Associative Rings by : V. Kharchenko
Download or read book Automorphisms and Derivations of Associative Rings written by V. Kharchenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras. The book consists of two parts. The first studies the geometry of indefinite metric spaces (Krein and (Pi)(kappa)-spaces) and describes the theory of J-symmetric operator algebras and representations of *-algebras and groups on these spaces in a systematic form. For representations on (Pi)(kappa)-spaces, many significant new results are obtained; this establishes a possible approach to the general theory of representations. In the second part, different techniques of the theory of J-symmetric representations on Krein spaces are applied to the theory of *-derivations of C*-algebras implemented by skew-symmetric and dissipative operators. Various results are obtained, which establish a link between the deficiency indices of skew-symmetric operators implementing *-derivations of C*-algebras and dimensions of representations of these algebras. The problem of isomorphism of skew-symmetric operators is also touched upon. Numerous properties of the domains of *-derivations are investigated. These domains constitute an important subclass of differentiable Banach *-algebras, that is dense *-subalgebras of C*-algebras with properties in many respects similar to the properties of algebras of differentiable functions. The Weyl operator commutation relations are examined in the general context of *-derivations of C*-algebras. Powersí and Arvesonís indices of one-parameter semigroups of *-endomorphisms of the algebra B are considered, and various notions of the index of a *-derivation are introduced and studied. Application of the theory of J-symmetric representations on Krein spaces to the theory of *-derivations of C*-algebras is a new research area of growing interest and there are many exciting advances to be made in this field. The book covers a fairly large and complex body of material, and will serve as a stimulus to further research activity in this area.
Book Synopsis Representations on Krein Spaces [Hot] and Derivations of C*-Algebras by : Edward Kissin
Download or read book Representations on Krein Spaces [Hot] and Derivations of C*-Algebras written by Edward Kissin and published by CRC Press. This book was released on 1997-10-03 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras. The book consists of two parts. The first studies the geometry of indefinite metric spaces (Krein and (Pi)(kappa)-spaces) and describes the theory of J-symmetric operator algebras and representations of *-algebras and groups on these spaces in a systematic form. For representations on (Pi)(kappa)-spaces, many significant new results are obtained; this establishes a possible approach to the general theory of representations. In the second part, different techniques of the theory of J-symmetric representations on Krein spaces are applied to the theory of *-derivations of C*-algebras implemented by skew-symmetric and dissipative operators. Various results are obtained, which establish a link between the deficiency indices of skew-symmetric operators implementing *-derivations of C*-algebras and dimensions of representations of these algebras. The problem of isomorphism of skew-symmetric operators is also touched upon. Numerous properties of the domains of *-derivations are investigated. These domains constitute an important subclass of differentiable Banach *-algebras, that is dense *-subalgebras of C*-algebras with properties in many respects similar to the properties of algebras of differentiable functions. The Weyl operator commutation relations are examined in the general context of *-derivations of C*-algebras. Powersí and Arvesonís indices of one-parameter semigroups of *-endomorphisms of the algebra B are considered, and various notions of the index of a *-derivation are introduced and studied. Application of the theory of J-symmetric representations on Krein spaces to the theory of *-derivations of C*-algebras is a new research area of growing interest and there are many exciting advances to be made in this field. The book covers a fairly large and complex body of material, and will serve as a stimulus to further research activity in this area.
This paper studies derivations, endomorphisms, automorphisms, and various related questions about certain Banach algebras, B, which are continuously embedded in the space of complex formal power series in the indeterminate z.
Book Synopsis Derivations and Automorphisms of Banach Algebras of Power Series by : Sandy Grabiner
Download or read book Derivations and Automorphisms of Banach Algebras of Power Series written by Sandy Grabiner and published by American Mathematical Soc.. This book was released on 1974 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies derivations, endomorphisms, automorphisms, and various related questions about certain Banach algebras, B, which are continuously embedded in the space of complex formal power series in the indeterminate z.
This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.
Book Synopsis Hasse-Schmidt Derivations on Grassmann Algebras by : Letterio Gatto
Download or read book Hasse-Schmidt Derivations on Grassmann Algebras written by Letterio Gatto and published by Springer. This book was released on 2016-07-08 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.
Hisatsugu Kitahara advances Noam Chomsky's Minimalist Program (1995) with a number of innovative proposals.
Book Synopsis Elementary Operations and Optimal Derivations by : Hisatsugu Kitahara
Download or read book Elementary Operations and Optimal Derivations written by Hisatsugu Kitahara and published by MIT Press. This book was released on 1997 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hisatsugu Kitahara advances Noam Chomsky's Minimalist Program (1995) with a number of innovative proposals.
Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in prepara tion of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.
Book Synopsis Simple Theorems, Proofs, and Derivations in Quantum Chemistry by : Istvan Mayer
Download or read book Simple Theorems, Proofs, and Derivations in Quantum Chemistry written by Istvan Mayer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in prepara tion of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.
This study shows that Scandinavian object shift and so-called A-scrambling in the continental Germanic languages are the same, and aims at providing an account of the variation that we find with respect to this phenomenon by combining certain aspects of the Minimalist Program and Optimality Theory. More specifically, it is claimed that representations created by a simplified version of the computational system of human language CHL are evaluated in an optimality theoretic fashion by taking recourse to a very small set of output constraints.
Book Synopsis Derivations and Evaluations by : Hans Broekhuis
Download or read book Derivations and Evaluations written by Hans Broekhuis and published by Walter de Gruyter. This book was released on 2008-08-27 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study shows that Scandinavian object shift and so-called A-scrambling in the continental Germanic languages are the same, and aims at providing an account of the variation that we find with respect to this phenomenon by combining certain aspects of the Minimalist Program and Optimality Theory. More specifically, it is claimed that representations created by a simplified version of the computational system of human language CHL are evaluated in an optimality theoretic fashion by taking recourse to a very small set of output constraints.
