Hopf Algebras And Their Actions On Rings

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Hopf Algebras and Their Actions on Rings

Susan Montgomery
Hopf Algebras and Their Actions on Rings Book PDF

Author : Susan Montgomery
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 42,8 Mb
Release : 1993-10-28
Category : Mathematics
ISBN : 9780821807385

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Hopf Algebras and Their Actions on Rings by Susan Montgomery Pdf

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 and Their Generalizations from a Category Theoretical Point of View

Gabriella Böhm
Hopf Algebras and Their Generalizations from a Category Theoretical Point of View Book PDF

Author : Gabriella Böhm
Publisher : Springer
Page : 165 pages
File Size : 54,8 Mb
Release : 2018-11-01
Category : Mathematics
ISBN : 9783319981376

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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View by Gabriella Böhm Pdf

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.

Rings, Hopf Algebras, and Brauer Groups

Stefaan Caenepeel
Rings Hopf Algebras and Brauer Groups Book PDF

Author : Stefaan Caenepeel
Publisher : CRC Press
Page : 128 pages
File Size : 50,9 Mb
Release : 2020-09-30
Category : Mathematics
ISBN : 9781000116731

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Rings, Hopf Algebras, and Brauer Groups by Stefaan Caenepeel Pdf

"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

Groups, Rings, Lie and Hopf Algebras

Y. Bahturin
Groups Rings Lie and Hopf Algebras Book PDF

Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 45,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302353

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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.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya M. Gubareni
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 388 pages
File Size : 52,5 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482245059

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Groups, Rings, Group Rings, and Hopf Algebras

Jeffrey Bergen,Stefan Catoiu,William Chin
Groups Rings Group Rings and Hopf Algebras Book PDF

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 45,8 Mb
Release : 2017-04-24
Category : Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals
ISBN : 9781470428051

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Groups, Rings, Group Rings, and Hopf Algebras by Jeffrey Bergen,Stefan Catoiu,William Chin Pdf

This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2–4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3–4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.

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 : 46,7 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.

Hopf Algebras

David E. Radford
Hopf Algebras Book PDF

Author : David E. Radford
Publisher : World Scientific
Page : 584 pages
File Size : 52,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814335997

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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.

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 : 52,6 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.

Fundamentals of Hopf Algebras

Robert G. Underwood
Fundamentals of Hopf Algebras Book PDF

Author : Robert G. Underwood
Publisher : Springer
Page : 164 pages
File Size : 41,5 Mb
Release : 2015-06-10
Category : Mathematics
ISBN : 9783319189918

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Fundamentals of Hopf Algebras by Robert G. Underwood Pdf

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.

Quasi-Hopf Algebras

Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen
Quasi Hopf Algebras Book PDF

Author : Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen
Publisher : Cambridge University Press
Page : 545 pages
File Size : 54,8 Mb
Release : 2019-02-21
Category : Mathematics
ISBN : 9781108427012

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Quasi-Hopf Algebras by Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen Pdf

This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.

Group Actions on Rings

Susan Montgomery
Group Actions on Rings Book PDF

Author : Susan Montgomery
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 42,9 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850466

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Group Actions on Rings by Susan Montgomery Pdf

Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.

An Introduction to Hopf Algebras

Robert G. Underwood
An Introduction to Hopf Algebras Book PDF

Author : Robert G. Underwood
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 41,6 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 9780387727653

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An Introduction to Hopf Algebras by Robert G. Underwood Pdf

Only book on Hopf algebras aimed at advanced undergraduates

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 : 44,8 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. "

Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

Lindsay Childs
Hopf Algebras Polynomial Formal Groups and Raynaud Orders Book PDF

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 50,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.