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Author: Christopher David Walker
Publisher:
ISBN:
Category : Hopf algebras
Languages : en
Pages : 124
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Book Description
The Nichols-Zoeller freeness theorem states that a finite dimensional Hopf algebra is free as a module over any subHopfalgebra. We will prove this theorem, as well as the first significant generalization of this theorem, which was proven three years later. This generalization says that if the Hopf algebra is infinite dimensional, then the Hopf algebra is still free if the subHopfalgebra is finite dimensional and semisimple . We will also look at several other significant generalizations that have since been proven.
Author: Christopher David Walker
Publisher:
ISBN:
Category : Hopf algebras
Languages : en
Pages : 124
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Book Description
The Nichols-Zoeller freeness theorem states that a finite dimensional Hopf algebra is free as a module over any subHopfalgebra. We will prove this theorem, as well as the first significant generalization of this theorem, which was proven three years later. This generalization says that if the Hopf algebra is infinite dimensional, then the Hopf algebra is still free if the subHopfalgebra is finite dimensional and semisimple . We will also look at several other significant generalizations that have since been proven.
Author: M. Bettina Zoeller
Publisher:
ISBN:
Category : Group algebras
Languages : en
Pages : 172
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Book Description
Author: Susan Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821807382
Category : Mathematics
Languages : en
Pages : 258
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Book Description
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.
Author: Jeffrey Bergen
Publisher:
ISBN: 9781003419792
Category : MATHEMATICS
Languages : en
Pages : 0
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Book Description
This remarkable reference contains expository papers by leading researchers in the field of Hopf algebras, most of which were presented at the National Science Foundation-Conference Board of the Mathematical Sciences symposium on Hopf algebras held at DePaul University, Chicago, Illinois. Discussing connections of Hopf algebras to other areas of mathematics, including category theory, group theory, combinatorics, and the theory of knots and links in topology, Advances in Hopf Algebras offers positive results on local freeness built around the Hopf algebra theme...covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras...examines the actions of quasitriangular Hopf algebras on quantum-commutative algebras...studies some general principles on how to construct algebras and comodule algebras... constructs endomorphism spaces in the category of noncommutative spaces...describes quantum GL[subscript d] and introduces the q-Schur algebra with the Hecke algebra...investigates the Knot invariance arising from finite-dimensional ribbon Hopf algebras and the algebra involved in their construction...and more. Furnishing over 800 up-to-date literature citations, useful equations, and helpful drawings, Advances in Hopf Algebras is a vital resource for algebraists, noncommutative ring theorists, number theorists, theoretical physicists, and upper-level undergraduate and graduate students in these disciplines.
Author: David E Radford
Publisher: World Scientific
ISBN: 9814405108
Category : Mathematics
Languages : en
Pages : 584
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Book Description
The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.
Author: Jeffrey Bergen
Publisher: CRC Press
ISBN: 1000938891
Category : Mathematics
Languages : en
Pages : 344
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Book Description
"This remarkable reference covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras. "
Author: Daniel Bulacu
Publisher: Cambridge University Press
ISBN: 1108427014
Category : Mathematics
Languages : en
Pages : 545
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Book Description
This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 1482276712
Category : Mathematics
Languages : en
Pages : 344
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Book Description
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Author: Lindsay N. Childs
Publisher: American Mathematical Soc.
ISBN: 1470465167
Category : Education
Languages : en
Pages : 311
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Book Description
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Author: Jeffrey Bergen
Publisher: CRC Press
ISBN: 9780824755669
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This volume publishes key proceedings from the recent International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois. With contributions from leading researchers in the field, this collection deals with current topics ranging from categories of infinitesimal Hopf modules and bimodules to the construction of a Hopf algebraic Morita invariant. It uses the newly introduced theory of bi-Frobenius algebras to investigate a notion of group-like algebras and summarizes results on the classification of Hopf algebras of dimension pq. It also explores pre-Lie, dendriform, and Nichols algebras and discusses support cones for infinitesimal group schemes.
