Hopf Algebras And Root Systems

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Hopf Algebras and Root Systems

István Heckenberger,Hans-Jürgen Schneider
Hopf Algebras and Root Systems Book PDF

Author : István Heckenberger,Hans-Jürgen Schneider
Publisher : American Mathematical Soc.
Page : 582 pages
File Size : 53,8 Mb
Release : 2020-06-19
Category : Education
ISBN : 9781470452322

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Hopf Algebras and Root Systems by István Heckenberger,Hans-Jürgen Schneider Pdf

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.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko
Publisher : American Mathematical Soc.
Page : 425 pages
File Size : 40,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852620

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko Pdf

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.

Advances in Hopf Algebras

Jeffrey Bergen,Susan Montgomery
Advances in Hopf Algebras Book PDF

Author : Jeffrey Bergen,Susan Montgomery
Publisher : CRC Press
Page : 344 pages
File Size : 51,7 Mb
Release : 2023-08-18
Category : Mathematics
ISBN : 9781000938890

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Advances in Hopf Algebras by Jeffrey Bergen,Susan Montgomery Pdf

"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. "

New Directions in Hopf Algebras

Susan Montgomery,Hans-Jurgen Schneider
New Directions in Hopf Algebras Book PDF

Author : Susan Montgomery,Hans-Jurgen Schneider
Publisher : Cambridge University Press
Page : 502 pages
File Size : 48,6 Mb
Release : 2002-05-06
Category : Mathematics
ISBN : 0521815126

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New Directions in Hopf Algebras by Susan Montgomery,Hans-Jurgen Schneider Pdf

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.

Hopf Algebra

Sorin Dascalescu,Constantin Nastasescu,Serban Raianu
Hopf Algebra Book PDF

Author : Sorin Dascalescu,Constantin Nastasescu,Serban Raianu
Publisher : CRC Press
Page : 420 pages
File Size : 47,8 Mb
Release : 2000-09-15
Category : Mathematics
ISBN : 9781482270747

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Hopf Algebra by Sorin Dascalescu,Constantin Nastasescu,Serban Raianu Pdf

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.

Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order

Yorck Sommerhäuser
Yetter Drinfel d Hopf Algebras over Groups of Prime Order Book PDF

Author : Yorck Sommerhäuser
Publisher : Springer
Page : 164 pages
File Size : 52,5 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540454236

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Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order by Yorck Sommerhäuser Pdf

Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.

Groups, Rings, Lie and Hopf Algebras

Anonim
Groups Rings Lie and Hopf Algebras Book PDF

Author : Anonim
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 40,6 Mb
Release : 2003-03-31
Category : Mathematics
ISBN : 1402012209

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Groups, Rings, Lie and Hopf Algebras by Anonim Pdf

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Hopf Algebras

Jeffrey Bergen,Stefan Catoiu,William Chin
Hopf Algebras Book PDF

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : CRC Press
Page : 282 pages
File Size : 40,7 Mb
Release : 2004-01-28
Category : Mathematics
ISBN : 0824755669

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Hopf Algebras by Jeffrey Bergen,Stefan Catoiu,William Chin Pdf

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.

Hopf Algebras, Tensor Categories and Related Topics

Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Hopf Algebras Tensor Categories and Related Topics Book PDF

Author : Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 54,7 Mb
Release : 2021-07-06
Category : Education
ISBN : 9781470456245

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Hopf Algebras, Tensor Categories and Related Topics by Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang Pdf

The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.

Hopf Algebras

David E Radford
Hopf Algebras Book PDF

Author : David E Radford
Publisher : World Scientific
Page : 588 pages
File Size : 49,6 Mb
Release : 2011-12-28
Category : Mathematics
ISBN : 9789814405102

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Hopf Algebras by David E Radford Pdf

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. Contents:PreliminariesCoalgebrasRepresentations of CoalgebrasThe Coradical Filtration and Related StructuresBialgebrasThe Convolution AlgebraHopf AlgebrasHopf Modules and Co-Hopf ModulesHopf Algebras as Modules Over Their Hopf SubalgebrasIntegralsActions by Bialgebras and Hopf AlgebrasQuasitriangular Bialgebras and Hopf AlgebrasThe Drinfel'd Double of a Finite-Dimensional Hopf AlgebraCo-Quasitriangular Bialgebras and Hopf AlgebrasPointed Hopf AlgebrasFinite-Dimensional Hopf Algebras in Characteristic 0 Readership: Undergraduates and researchers in algebra and number theory. Keywords:Hopf Algebras;Coalgebras;Quantum GroupsKey Features:Provides a good foundation for those who wish to study Hopf algebras on their ownProvides a firm foundation for those who are more interested in applications to other areasGives many exercises which suggest connections to exploreReviews: "With this monograph, one of the pioneers of the subject provides a comprehensive introduction to the theory of Hopf algebras. As this theory has made great strides in recent years, such a monograph constitutes a very valuable addition to the literature, especially as there are so far comparatively few textbooks on this topic. Radford's book contains at the end of each chapter a very useful set of chapter notes that discuss these references and therefore provide an entry point to the recent research literature, especially to the extensive literature on the classification of finite–dimensional pointed Hopf algebras, a topic not discussed in any of the other books. For all these reasons, Radford's book is a very valuable new textbook on Hopf algebras that will be frequently used both by students and by researchers." Mathematical Reviews "A big number of exercises of different level of difficulty are proposed along the text, which include in particular special features or applications to a variety of concrete examples, further results and categorical aspects of the corresponding material. Interesting and up-to-date historical and bibliographical comments are provided at the end of each of the sixteen chapters." Zentralblatt MATH

Tensor Categories and Hopf Algebras

Nicolás Andruskiewitsch,Dmitri Nikshych
Tensor Categories and Hopf Algebras Book PDF

Author : Nicolás Andruskiewitsch,Dmitri Nikshych
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 50,7 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781470443214

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Tensor Categories and Hopf Algebras by Nicolás Andruskiewitsch,Dmitri Nikshych Pdf

This volume contains the proceedings of the scientific session “Hopf Algebras and Tensor Categories”, held from July 27–28, 2017, at the Mathematical Congress of the Americas in Montreal, Canada. Papers highlight the latest advances and research directions in the theory of tensor categories and Hopf algebras. Primary topics include classification and structure theory of tensor categories and Hopf algebras, Gelfand-Kirillov dimension theory for Nichols algebras, module categories and weak Hopf algebras, Hopf Galois extensions, graded simple algebras, and bialgebra coverings.




Classical Hopf Algebras and Their Applications

Pierre Cartier,Frédéric Patras
Classical Hopf Algebras and Their Applications Book PDF

Author : Pierre Cartier,Frédéric Patras
Publisher : Springer Nature
Page : 277 pages
File Size : 49,9 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9783030778453

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Classical Hopf Algebras and Their Applications by Pierre Cartier,Frédéric Patras Pdf

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 Algebra

Sorin Dascalescu,Constantin Nastasescu,Serban Raianu
Hopf Algebra Book PDF

Author : Sorin Dascalescu,Constantin Nastasescu,Serban Raianu
Publisher : CRC Press
Page : 428 pages
File Size : 43,5 Mb
Release : 2000-09-15
Category : Mathematics
ISBN : 0824704819

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Hopf Algebra by Sorin Dascalescu,Constantin Nastasescu,Serban Raianu Pdf

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.

Groups, Rings, Lie and Hopf Algebras

Y. Bahturin
Groups Rings Lie and Hopf Algebras Book PDF

Author : Y. Bahturin
Publisher : Springer
Page : 0 pages
File Size : 46,6 Mb
Release : 2011-09-17
Category : Mathematics
ISBN : 1461379547

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Groups, Rings, Lie and Hopf Algebras by Y. Bahturin Pdf

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations

Florin Felix Nichita
Hopf Algebras Quantum Groups and Yang Baxter Equations Book PDF

Author : Florin Felix Nichita
Publisher : MDPI
Page : 239 pages
File Size : 52,8 Mb
Release : 2019-01-31
Category : Mathematics
ISBN : 9783038973249

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Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita Pdf

This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms