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Rings, Hopf Algebras, and Brauer Groups

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2020-09-30

Total Pages:

ISBN-13: 1000116735

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"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Book Synopsis Rings, Hopf Algebras, and Brauer Groups by : Stefaan Caenepeel

Download or read book Rings, Hopf Algebras, and Brauer Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-09-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Brauer Groups, Hopf Algebras and Galois Theory

Author: Stefaan Caenepeel

Publisher: Springer Science & Business Media

Published: 2002-03-31

Total Pages: 516

ISBN-13: 9781402003462

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This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Book Synopsis Brauer Groups, Hopf Algebras and Galois Theory by : Stefaan Caenepeel

Download or read book Brauer Groups, Hopf Algebras and Galois Theory written by Stefaan Caenepeel and published by Springer Science & Business Media. This book was released on 2002-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Rings, Hopf Algebras, and Brauer Groups

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2020-09-29

Total Pages: 352

ISBN-13: 1000153282

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Book Synopsis Rings, Hopf Algebras, and Brauer Groups by : Stefaan Caenepeel

Download or read book Rings, Hopf Algebras, and Brauer Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-09-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Algebras, Rings and Modules

Author: Michiel Hazewinkel

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 425

ISBN-13: 0821852620

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Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.

Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel

Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by American Mathematical Soc.. This book was released on 2010 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.

Groups, Rings, Lie and Hopf Algebras

Author: Y. Bahturin

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 240

ISBN-13: 1461302358

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Book Synopsis Groups, Rings, Lie and Hopf Algebras by : Y. Bahturin

Download or read book Groups, Rings, Lie and Hopf Algebras written by Y. Bahturin and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Brauer Groups and the Cohomology of Graded Rings

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2020-08-27

Total Pages: 283

ISBN-13: 1000147215

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This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.

Book Synopsis Brauer Groups and the Cohomology of Graded Rings by : Stefaan Caenepeel

Download or read book Brauer Groups and the Cohomology of Graded Rings written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-08-27 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.

Groups, Rings, Lie and Hopf Algebras

Author:

Publisher: Springer Science & Business Media

Published: 2003-03-31

Total Pages: 266

ISBN-13: 9781402012204

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Book Synopsis Groups, Rings, Lie and Hopf Algebras by :

Download or read book Groups, Rings, Lie and Hopf Algebras written by and published by Springer Science & Business Media. This book was released on 2003-03-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Hopf Algebras and Their Actions on Rings

Author: Susan Montgomery

Publisher: American Mathematical Soc.

Published: 1993-10-28

Total Pages: 258

ISBN-13: 0821807382

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The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

Book Synopsis Hopf Algebras and Their Actions on Rings by : Susan Montgomery

Download or read book Hopf Algebras and Their Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1993-10-28 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

Brauer Groups

Author: D. Zelinsky

Publisher: Springer

Published: 2006-11-14

Total Pages: 193

ISBN-13: 3540379789

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Book Synopsis Brauer Groups by : D. Zelinsky

Download or read book Brauer Groups written by D. Zelinsky and published by Springer. This book was released on 2006-11-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: a

Brauer Groups of H-dimodule Algebras and Truncated Power Series Hopf Algebras

Author: Richard Beng-Tok Tan

Publisher:

Published: 1980

Total Pages: 110

ISBN-13:

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Book Synopsis Brauer Groups of H-dimodule Algebras and Truncated Power Series Hopf Algebras by : Richard Beng-Tok Tan

Download or read book Brauer Groups of H-dimodule Algebras and Truncated Power Series Hopf Algebras written by Richard Beng-Tok Tan and published by . This book was released on 1980 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: