Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Download The Gelfand Kirillov Dimension Of Rank 2 Nichols Algebras Of Diagonal Type full books in PDF, epub, and Kindle. Read online The Gelfand Kirillov Dimension Of Rank 2 Nichols Algebras Of Diagonal Type ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author : Eric Heymann-Heidelberger
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (117 download)
Download or read book The Gelfand-Kirillov Dimension of Rank 2 Nichols Algebras of Diagonal Type written by Eric Heymann-Heidelberger and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : István Heckenberger
Publisher : American Mathematical Soc.
ISBN 13 : 1470452324
Total Pages : 582 pages
Book Rating : 4.4/5 (74 download)
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 582 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.
Author : Nicolás Andruskiewitsch
Publisher : American Mathematical Soc.
ISBN 13 : 147044321X
Total Pages : 194 pages
Book Rating : 4.4/5 (74 download)
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 194 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.
Author : Anton Alekseev
Publisher : Springer Nature
ISBN 13 : 3030781488
Total Pages : 652 pages
Book Rating : 4.0/5 (37 download)
Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
Download or read book (Avis donné aux cinquanteniers de la ville de Paris, de la part de Robert de Brie, dizainier et bourgeois de Paris, d'avoir à verser chacun la somme de 30 sols, pour subvenir aux frais nécessités par la conservation de leurs privilèges.). written by and published by . This book was released on 1665 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jun Wang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)
Download or read book Affine Rank Two Nichols Algebras of Diagonal Type written by Jun Wang and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jing Wang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (956 download)
Download or read book Finite Dimensional Nichols Algebras of Diagonal Type Over Fields of Positive Characteristic written by Jing Wang and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)
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.
Author : Alexander Cardona
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 347 pages
Book Rating : 4.3/5 (196 download)
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.
Author : G. R. Krause
Publisher : American Mathematical Soc.
ISBN 13 : 0821808591
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author : Steven Duplij
Publisher : Springer Science & Business Media
ISBN 13 : 9780792369981
Total Pages : 504 pages
Book Rating : 4.3/5 (699 download)
Download or read book Noncommutative Structures in Mathematics and Physics written by Steven Duplij and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
Author : Anthony E. Clement
Publisher : Birkhäuser
ISBN 13 : 3319662139
Total Pages : 318 pages
Book Rating : 4.3/5 (196 download)
Download or read book The Theory of Nilpotent Groups written by Anthony E. Clement and published by Birkhäuser. This book was released on 2017-11-18 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.
Author : Nolan R. Wallach
Publisher : Academic Press
ISBN 13 : 0080874517
Total Pages : 439 pages
Book Rating : 4.0/5 (88 download)
Download or read book Real Reductive Groups I written by Nolan R. Wallach and published by Academic Press. This book was released on 1988-03-01 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.
Author : Sonia Natale
Publisher : American Mathematical Soc.
ISBN 13 : 0821839489
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)
Download or read book Semisolvability of Semisimple Hopf Algebras of Low Dimension written by Sonia Natale and published by American Mathematical Soc.. This book was released on 2007 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
Author : M. J. Tomkinson
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (45 download)
Download or read book FC-groups written by M. J. Tomkinson and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Lusztig
Publisher : Springer Science & Business Media
ISBN 13 : 0817647171
Total Pages : 361 pages
Book Rating : 4.8/5 (176 download)
Download or read book Introduction to Quantum Groups written by George Lusztig and published by Springer Science & Business Media. This book was released on 2010-10-27 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
