Hopf Algebra

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Classical Hopf Algebras And Their Applications

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Author : Pierre Cartier
language : en
Publisher: Springer Nature
Release Date : 2021-09-20

Classical Hopf Algebras And Their Applications written by Pierre Cartier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Mathematics categories.

This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.

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

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.

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.

Hopf Algebras And Generalizations

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Author : Louis H. Kauffman
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Hopf Algebras And Generalizations written by Louis H. Kauffman 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 2007 with Mathematics categories.

Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.

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.

Notes from a course given in the spring of 1968 at Cornell University.

Advances In Hopf Algebras

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Author : Jeffrey Bergen
language : en
Publisher: CRC Press
Release Date : 2023-08-18

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 2023-08-18 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 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.

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.