Hopf Algebras Of Finite Gelfand Kirillov Dimension

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Hopf Algebras

Author : Jeffrey Bergen
Publisher : CRC Press
ISBN 13 : 9780824755669
Total Pages : 282 pages
Book Rating : 4.7/5 (556 download)

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Book Synopsis Hopf Algebras by : Jeffrey Bergen

Download or read book Hopf Algebras written by Jeffrey Bergen and published by CRC Press. This book was released on 2004-01-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On Finite GK-Dimensional Nichols Algebras over Abelian Groups

Author : Nicol s Andruskiewitsch
Publisher : American Mathematical Society
ISBN 13 : 1470448300
Total Pages : 125 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On Finite GK-Dimensional Nichols Algebras over Abelian Groups by : Nicol s Andruskiewitsch

Download or read book On Finite GK-Dimensional Nichols Algebras over Abelian Groups written by Nicol s Andruskiewitsch and published by American Mathematical Society. This book was released on 2021-09-24 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Tensor Categories and Hopf Algebras

Author : Nicolás Andruskiewitsch
Publisher : American Mathematical Soc.
ISBN 13 : 147044321X
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tensor Categories and Hopf Algebras by : Nicolás Andruskiewitsch

Download or read book Tensor Categories and Hopf Algebras written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2019-04-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Hopf Algebras and Root Systems

Author : István Heckenberger
Publisher : American Mathematical Soc.
ISBN 13 : 1470452324
Total Pages : 606 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hopf Algebras and Root Systems by : István Heckenberger

Download or read book Hopf Algebras and Root Systems written by István Heckenberger and published by American Mathematical Soc.. This book was released on 2020-06-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Growth of Algebras and Gelfand-Kirillov Dimension

Author : G. R. Krause
Publisher : American Mathematical Soc.
ISBN 13 : 0821808591
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Growth of Algebras and Gelfand-Kirillov Dimension by : G. R. Krause

Download or read book Growth of Algebras and Gelfand-Kirillov Dimension written by G. R. Krause and published by American Mathematical Soc.. This book was released on 2000 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the two decades that preceded the publication of the first edition of this book, the Gelfand-Kirillov dimension had emerged as a very useful and powerful tool for investigating non-commutative algebras. At that time, the basic ideas and results were scattered throughout various journal articles. The first edition of this book provided a much-needed reliable and coherent single source of information. Since that time, the book has become the standard reference source for researchers. For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last few years, with references to the literature for details. The bibliography has been updated and accordingly, almost double the size of the original one. The faithful revision and contemporary design of this work offers time-honored expertise with modern functionality. A keenly appealing combination. So, whether for the classroom, the well-tended mathematical books collection, or the research desk, this book holds unprecedented relevance.

Hopf Algebras, Tensor Categories and Related Topics

Author : Nicolás Andruskiewitsch
Publisher : American Mathematical Soc.
ISBN 13 : 1470456249
Total Pages : 359 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hopf Algebras, Tensor Categories and Related Topics by : Nicolás Andruskiewitsch

Download or read book Hopf Algebras, Tensor Categories and Related Topics written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2021-07-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representation Theory

Author : Zongzhu Lin
Publisher : American Mathematical Soc.
ISBN 13 : 0821845551
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory by : Zongzhu Lin

Download or read book Representation Theory written by Zongzhu Lin and published by American Mathematical Soc.. This book was released on 2009-01-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided

New Directions in Hopf Algebras

Author : Susan Montgomery
Publisher : Cambridge University Press
ISBN 13 : 9780521815123
Total Pages : 502 pages
Book Rating : 4.8/5 (151 download)

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Book Synopsis New Directions in Hopf Algebras by : Susan Montgomery

Download or read book New Directions in Hopf Algebras written by Susan Montgomery and published by Cambridge University Press. This book was released on 2002-05-06 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Groups, Rings, Lie and Hopf Algebras

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9781402012204
Total Pages : 266 pages
Book Rating : 4.0/5 (122 download)

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Book Synopsis Groups, Rings, Lie and Hopf Algebras by :

Download or read book Groups, Rings, Lie and Hopf Algebras written by and published by Springer Science & Business Media. This book was released on 2003-03-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rings, Hopf Algebras, and Brauer Groups

Author : Stefaan Caenepeel
Publisher : CRC Press
ISBN 13 : 1000153282
Total Pages : 352 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Rings, Hopf Algebras, and Brauer Groups by : Stefaan Caenepeel

Download or read book Rings, Hopf Algebras, and Brauer Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-09-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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. "

Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

Author : Alexander Cardona
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 347 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona

Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.

Algorithmic Methods in Non-Commutative Algebra

Author : J.L. Bueso
Publisher : Springer Science & Business Media
ISBN 13 : 9401702853
Total Pages : 307 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Algorithmic Methods in Non-Commutative Algebra by : J.L. Bueso

Download or read book Algorithmic Methods in Non-Commutative Algebra written by J.L. Bueso and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.

Lectures on Algebraic Quantum Groups

Author : Ken Brown
Publisher : Birkhäuser
ISBN 13 : 303488205X
Total Pages : 339 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Lectures on Algebraic Quantum Groups by : Ken Brown

Download or read book Lectures on Algebraic Quantum Groups written by Ken Brown and published by Birkhäuser. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Groups, Rings, Group Rings, and Hopf Algebras

Author : Jeffrey Bergen
Publisher : American Mathematical Soc.
ISBN 13 : 1470428059
Total Pages : 294 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Groups, Rings, Group Rings, and Hopf Algebras by : Jeffrey Bergen

Download or read book Groups, Rings, Group Rings, and Hopf Algebras written by Jeffrey Bergen and published by American Mathematical Soc.. This book was released on 2017-04-24 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebra - Representation Theory

Author : Klaus W. Roggenkamp
Publisher : Springer Science & Business Media
ISBN 13 : 9780792371137
Total Pages : 488 pages
Book Rating : 4.3/5 (711 download)

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Book Synopsis Algebra - Representation Theory by : Klaus W. Roggenkamp

Download or read book Algebra - Representation Theory written by Klaus W. Roggenkamp and published by Springer Science & Business Media. This book was released on 2001-08-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.

Trends in the Representation Theory of Finite Dimensional Algebras

Author : Edward L. Green
Publisher : American Mathematical Soc.
ISBN 13 : 0821809288
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Trends in the Representation Theory of Finite Dimensional Algebras by : Edward L. Green

Download or read book Trends in the Representation Theory of Finite Dimensional Algebras written by Edward L. Green and published by American Mathematical Soc.. This book was released on 1998 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.

Tensor Categories

Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.