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| Author | : Nicolás Andruskiewitsch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 359 |
| Release | : 2021-07-06 |
| Genre | : Education |
| ISBN | : 1470456249 |
Download Hopf Algebras, Tensor Categories and Related Topics Book in PDF, ePub and Kindle
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.
| Author | : Pavel Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2016-08-05 |
| Genre | : Mathematics |
| ISBN | : 1470434415 |
Download Tensor Categories Book in PDF, ePub and Kindle
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 | : Nicolás Andruskiewitsch |
| Publisher | : |
| Total Pages | : 210 |
| Release | : 2019 |
| Genre | : Electronic books |
| ISBN | : 9781470452391 |
Download Tensor Categories and Hopf Algebras Book in PDF, ePub and Kindle
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 | : Nicolás Andruskiewitsch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 194 |
| Release | : 2019-04-18 |
| Genre | : Mathematics |
| ISBN | : 147044321X |
Download Tensor Categories and Hopf Algebras Book in PDF, ePub and Kindle
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 | : Chengming Bai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2013-10-30 |
| Genre | : Mathematics |
| ISBN | : 3642393837 |
Download Conformal Field Theories and Tensor Categories Book in PDF, ePub and Kindle
The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
| Author | : Nicolás Andruskiewitsch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 347 |
| Release | : 2013-02-21 |
| Genre | : Mathematics |
| ISBN | : 0821875647 |
Download Hopf Algebras and Tensor Categories Book in PDF, ePub and Kindle
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.
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2015 |
| Genre | : Algebraic topology |
| ISBN | : 9781470423490 |
Download Tensor categories Book in PDF, ePub and Kindle
| Author | : Aaron Wootton |
| Publisher | : American Mathematical Society |
| Total Pages | : 366 |
| Release | : 2022-02-03 |
| Genre | : Mathematics |
| ISBN | : 1470460254 |
Download Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics Book in PDF, ePub and Kindle
Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
| Author | : Benjamin Enriquez |
| Publisher | : European Mathematical Society |
| Total Pages | : 148 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783037190470 |
Download Quantum Groups Book in PDF, ePub and Kindle
The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.
| Author | : Susan Montgomery |
| Publisher | : Cambridge University Press |
| Total Pages | : 502 |
| Release | : 2002-05-06 |
| Genre | : Mathematics |
| ISBN | : 9780521815123 |
Download New Directions in Hopf Algebras Book in PDF, ePub and Kindle
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.
