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Hopf Algebras, Tensor Categories and Related Topics

2021-07-06 Education
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Release : 2021-07-06
Genre : Education
Kind : eBook
Book Rating : 249/5 ( reviews)

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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. This book was released on 2021-07-06. 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.

Tensor Categories and Hopf Algebras

2019 Electronic books
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Release : 2019
Genre : Electronic books
Kind : eBook
Book Rating : 391/5 ( reviews)

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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. This book was released on 2019. 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.

Tensor Categories

2016-08-05 Mathematics
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Release : 2016-08-05
Genre : Mathematics
Kind : eBook
Book Rating : 415/5 ( reviews)

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Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof. This book was released on 2016-08-05. 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.

Tensor Categories and Hopf Algebras

2019-04-18 Mathematics
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Release : 2019-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 21X/5 ( reviews)

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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. This book was released on 2019-04-18. 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.




Conformal Field Theories and Tensor Categories

2013-10-30 Mathematics
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Release : 2013-10-30
Genre : Mathematics
Kind : eBook
Book Rating : 837/5 ( reviews)

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Book Synopsis Conformal Field Theories and Tensor Categories by : Chengming Bai

Download or read book Conformal Field Theories and Tensor Categories written by Chengming Bai. This book was released on 2013-10-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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