Hopf Algebras And Tensor Categories
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Tensor Categories
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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05
Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
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.
Hopf Algebras Tensor Categories And Related Topics
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-06
Hopf Algebras Tensor Categories And Related Topics written by Nicolás Andruskiewitsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-06 with Education categories.
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.
Tensor Categories And Hopf Algebras
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-18
Tensor Categories And Hopf Algebras written by Nicolás Andruskiewitsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.
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.
Tensor Categories And Hopf Algebras
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Author : Nicolás Andruskiewitsch
language : en
Publisher:
Release Date : 2019
Tensor Categories And Hopf Algebras written by Nicolás Andruskiewitsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Electronic books categories.
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 Tensor Categories
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-21
Hopf Algebras And Tensor Categories written by Nicolás Andruskiewitsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
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.
Quasi Hopf Algebras
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Author : Daniel Bulacu
language : en
Publisher: Cambridge University Press
Release Date : 2019-02-21
Quasi Hopf Algebras written by Daniel Bulacu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.
This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.
Quantum Groups
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Author : Christian Kassel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Groups written by Christian Kassel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
Hopf Algebras And Quantum Groups
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Author : Stefaan Caenepeel
language : en
Publisher: CRC Press
Release Date : 2000-04-05
Hopf Algebras And Quantum Groups written by Stefaan Caenepeel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Science categories.
This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum groups.
Quantum Groups Hopf Algebras And Applications
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Author : Susan Montgomery
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-13
Quantum Groups Hopf Algebras And Applications written by Susan Montgomery and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-13 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Quantum Groups, Hopf Algebras, and Applications (in memory of Professor Earl J. Taft), which was held from October 22?23, 2022, at the University of Utah, Salt Lake City, Utah. Hopf algebras play a crucial role in many areas of mathematics, from finite groups to tensor categories, and allows researchers to make many connections between these subjects. Applications of Hopf algebras to low dimensional topology, topological quantum field theory, and condensed matter physics provide further motivation for the study of representations of Hopf algebras and their generalizations. In memory of Earl Jay Taft, a pioneer of the theory of Hopf algebras, this volume collects research articles on Hopf algebras, quantum groups, and tensor categories contributed by prominent researchers. The articles in this volume manifest the diversity and richness of the subject and contain exciting new results which will certainly have applications to different areas of mathematics and physics.