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An Introduction To Hopf Algebras

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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.

An Introduction To Hopf Algebras

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Author : Robert G. Underwood
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-30

An Introduction To Hopf Algebras written by Robert G. Underwood and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Mathematics categories.

Only book on Hopf algebras aimed at advanced undergraduates

An Introduction To Hopf Algebras

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Author : Robert G. Underwood
language : en
Publisher: Springer
Release Date : 2011-08-31

An Introduction To 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 2011-08-31 with Mathematics categories.

Only book on Hopf algebras aimed at advanced undergraduates

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 Algebra

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

Hopf Algebras And Root Systems

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Author : István Heckenberger
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-06-19

Hopf Algebras And Root Systems written by István Heckenberger 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 2020-06-19 with Education categories.

This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.

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.

Algebras Rings And Modules

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Author : Michiel Hazewinkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Algebras Rings And Modules written by Michiel Hazewinkel 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 2010 with Mathematics categories.

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.

Hopf Algebras And Tensor Categories

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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-21

Hopf Algebras And Tensor Categories written by Nicolás Andruskiewitsch 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 2013-02-21 with Mathematics categories.

This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain. The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.

An Introduction To Quantum And Vassiliev Knot Invariants

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Author : David M. Jackson
language : en
Publisher: Springer
Release Date : 2019-05-04

An Introduction To Quantum And Vassiliev Knot Invariants written by David M. Jackson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-04 with Mathematics categories.

This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.

An Introduction To Hopf Algebras

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