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Author: Volodymyr V. Lyubashenko
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 197
ISBN-13: 0821813617
DOWNLOAD EBOOK →This book is intended for graduate students and research mathematicians interested in associative rings and algebras.
Author: Jeffrey Bergen
Publisher: CRC Press
Published: 2004-01-28
Total Pages: 200
ISBN-13: 1482293153
DOWNLOAD EBOOK →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
Author: Eiichi Abe
Publisher: Cambridge University Press
Published: 2004-06-03
Total Pages: 304
ISBN-13: 9780521604895
DOWNLOAD EBOOK →An introduction to the basic theory of Hopf algebras for those familiar with basic linear and commutative algebra.
Author: Susan Montgomery
Publisher: Cambridge University Press
Published: 2002-05-06
Total Pages: 502
ISBN-13: 9780521815123
DOWNLOAD EBOOK →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.
Author: David E. Radford
Publisher: World Scientific
Published: 2011
Total Pages: 584
ISBN-13: 9814338664
DOWNLOAD EBOOK →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: Sorin Dascalescu
Publisher: CRC Press
Published: 2000-09-15
Total Pages: 420
ISBN-13: 1482270749
DOWNLOAD EBOOK →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.
Author: Sorin Dascalescu
Publisher: CRC Press
Published: 2000-09-15
Total Pages: 428
ISBN-13: 9780824704810
DOWNLOAD EBOOK →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.
Author: Robert G. Underwood
Publisher: Springer
Published: 2015-06-10
Total Pages: 164
ISBN-13: 3319189913
DOWNLOAD EBOOK →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.
Author: Abdenacer Makhlouf
Publisher: John Wiley & Sons
Published: 2021-12-29
Total Pages: 338
ISBN-13: 1789450187
DOWNLOAD EBOOK →This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
Author: Jeffrey Bergen
Publisher: CRC Press
Published: 2023-08-18
Total Pages: 344
ISBN-13: 1000938891
DOWNLOAD EBOOK →"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. "
