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Hopf Algebras

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Hopf Algebras

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Author : David E. Radford
language : en
Publisher: World Scientific
Release Date : 2011

Hopf Algebras written by David E. Radford and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

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.

Hopf Algebra

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Author : Sorin Dascalescu
language : en
Publisher: CRC Press
Release Date : 2000-09-15

Hopf Algebra written by Sorin Dascalescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Mathematics categories.

This study covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory; and more.

Advances In Hopf Algebras

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Author : Jeffrey Bergen
language : en
Publisher: CRC Press
Release Date : 1994-04-19

Advances In Hopf Algebras written by Jeffrey Bergen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-19 with Mathematics categories.

"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. "

Hopf Algebras

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Author : Moss E. Sweedler
language : en
Publisher:
Release Date : 1969

Hopf Algebras written by Moss E. Sweedler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Hopf algebras categories.

Hopf Algebra

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Author : Sorin Dascalescu
language : en
Publisher: CRC Press
Release Date : 2000-09-15

Hopf Algebras

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Author : Jeffrey Bergen
language : en
Publisher: CRC Press
Release Date : 2004-01-28

Hopf Algebras written by Jeffrey Bergen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-28 with Mathematics categories.

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

New Directions In Hopf Algebras

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Author : Susan Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-06

New Directions In Hopf Algebras written by Susan Montgomery and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-06 with Mathematics categories.

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.

Fundamentals Of Hopf Algebras

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Author : Robert G. Underwood
language : en
Publisher: Springer
Release Date : 2015-06-10

Fundamentals Of Hopf Algebras written by Robert G. Underwood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-10 with Mathematics categories.

This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises. Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.

Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View

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Author : Gabriella Böhm
language : en
Publisher: Springer
Release Date : 2018-11-01

Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View written by Gabriella Böhm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-01 with Mathematics categories.

These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.

Hopf Algebras And Their Actions On Rings

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Author : Susan Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-10-28

Hopf Algebras And Their Actions On Rings written by Susan Montgomery and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-28 with Mathematics categories.

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.

Hopf Algebras

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