New Directions In Hopf Algebras

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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 : 54,9 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.

New Directions and Applications in Control Theory

Wijesuriya P. Dayawansa,Anders Lindquist,Yishao Zhou
New Directions and Applications in Control Theory Book PDF

Author : Wijesuriya P. Dayawansa,Anders Lindquist,Yishao Zhou
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 45,5 Mb
Release : 2005-08-31
Category : Technology & Engineering
ISBN : 3540239537

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New Directions and Applications in Control Theory by Wijesuriya P. Dayawansa,Anders Lindquist,Yishao Zhou Pdf

This volume contains a collection of papers in control theory and applications presented at a conference in honor of Clyde Martin on the occasion of his 60th birthday, held in Lubbock, Texas, November 14-15, 2003.

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 : 51,8 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

David E. Radford
Hopf Algebras Book PDF

Author : David E. Radford
Publisher : World Scientific
Page : 584 pages
File Size : 52,6 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.

Hopf Algebras and Generalizations

Louis H. Kauffman,David E. Radford,Fernando José Oliveira Souza
Hopf Algebras and Generalizations Book PDF

Author : Louis H. Kauffman,David E. Radford,Fernando José Oliveira Souza
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 52,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838204

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Hopf Algebras and Generalizations by Louis H. Kauffman,David E. Radford,Fernando José Oliveira Souza Pdf

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, 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 : 50,6 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.

New Developments in Lie Theory and Its Applications

Carina Boyallian,Esther Galina,Linda Saal
New Developments in Lie Theory and Its Applications Book PDF

Author : Carina Boyallian,Esther Galina,Linda Saal
Publisher : American Mathematical Soc.
Page : 169 pages
File Size : 51,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852590

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New Developments in Lie Theory and Its Applications by Carina Boyallian,Esther Galina,Linda Saal Pdf

Focuses on representation theory, harmonic analysis in Lie groups, and mathematical physics related to Lie theory. The papers give a broad overview of these subjects and also of the recent developments in research.

Hopf Algebras in Noncommutative Geometry and Physics

Stefaan Caenepeel,Fred Van Oystaeyen
Hopf Algebras in Noncommutative Geometry and Physics Book PDF

Author : Stefaan Caenepeel,Fred Van Oystaeyen
Publisher : CRC Press
Page : 344 pages
File Size : 45,5 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9781482276718

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Hopf Algebras in Noncommutative Geometry and Physics by Stefaan Caenepeel,Fred Van Oystaeyen Pdf

This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the

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 : 46,5 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.

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 : 43,6 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.




Handbook of Algebra

Anonim
Handbook of Algebra Book PDF

Author : Anonim
Publisher : Elsevier
Page : 1184 pages
File Size : 51,9 Mb
Release : 2003-10-15
Category : Mathematics
ISBN : 0080532977

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Handbook of Algebra by Anonim Pdf

Handbook of Algebra

New Developments in Lie Theory and Geometry

Carolyn Gordon
New Developments in Lie Theory and Geometry Book PDF

Author : Carolyn Gordon
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 53,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846513

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New Developments in Lie Theory and Geometry by Carolyn Gordon Pdf

This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.

Handbook of Algebra

M. Hazewinkel
Handbook of Algebra Book PDF

Author : M. Hazewinkel
Publisher : Elsevier
Page : 577 pages
File Size : 40,8 Mb
Release : 2008-04-18
Category : Mathematics
ISBN : 9780080569413

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Handbook of Algebra by M. Hazewinkel Pdf

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

Hopf Algebras and Tensor Categories

Nicolás Andruskiewitsch,Juan Cuadra,Blas Torrecillas
Hopf Algebras and Tensor Categories Book PDF

Author : Nicolás Andruskiewitsch,Juan Cuadra,Blas Torrecillas
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 42,9 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780821875643

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Hopf Algebras and Tensor Categories by Nicolás Andruskiewitsch,Juan Cuadra,Blas Torrecillas Pdf

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.

Advances in Hopf Algebras

Jeffrey Bergen,Susan Montgomery
Advances in Hopf Algebras Book PDF

Author : Jeffrey Bergen,Susan Montgomery
Publisher : CRC Press
Page : 341 pages
File Size : 45,5 Mb
Release : 2023-08-18
Category : Mathematics
ISBN : 9781000944945

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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. "