Quasi-Hopf Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quasi-Hopf Algebras write by Daniel Bulacu. This book was released on 2019-02-21. Quasi-Hopf Algebras available in PDF, EPUB and Kindle. This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Quasi-Hopf Algebras
Quasi-Hopf Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quasi-Hopf Algebras write by Daniel Bulacu. This book was released on 2019-02-21. Quasi-Hopf Algebras available in PDF, EPUB and Kindle. 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.
Tensor Categories
Tensor Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Categories write by Pavel Etingof. This book was released on 2016-08-05. Tensor Categories available 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.
Quantum Groups
Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Groups write by Christian Kassel. This book was released on 2012-12-06. Quantum Groups available in PDF, EPUB and Kindle. 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 Tensor Categories
Hopf Algebras and Tensor Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hopf Algebras and Tensor Categories write by Nicolás Andruskiewitsch. This book was released on 2013-02-21. Hopf Algebras and Tensor Categories available 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.
