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Quasi-Hopf Algebras

Quasi-Hopf Algebras PDF Author: Daniel Bulacu
Publisher: Cambridge University Press
ISBN: 1108427014
Category : Mathematics
Languages : en
Pages : 545

Book Description
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 PDF Author: Daniel Bulacu
Publisher: Cambridge University Press
ISBN: 1108427014
Category : Mathematics
Languages : en
Pages : 545

Book Description
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 PDF Author: Daniel Bulacu
Publisher: Cambridge University Press
ISBN: 1108632653
Category : Mathematics
Languages : en
Pages : 546

Book Description
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 PDF Author: Pavel Etingof
Publisher: American Mathematical Soc.
ISBN: 1470434415
Category : Mathematics
Languages : en
Pages : 362

Book Description
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 PDF Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 1461207835
Category : Mathematics
Languages : en
Pages : 540

Book Description
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 PDF Author: Nicolás Andruskiewitsch
Publisher: American Mathematical Soc.
ISBN: 0821875647
Category : Mathematics
Languages : en
Pages : 347

Book Description
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.

Hopf Algebras

Hopf Algebras PDF Author: David E. Radford
Publisher: World Scientific
ISBN: 9814335991
Category : Mathematics
Languages : en
Pages : 584

Book Description
The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.

Hopf Algebras

Hopf Algebras PDF Author: Eiichi Abe
Publisher: Cambridge University Press
ISBN: 9780521604895
Category : Mathematics
Languages : en
Pages : 304

Book Description
An introduction to the basic theory of Hopf algebras for those familiar with basic linear and commutative algebra.

Hopf Algebras and Their Actions on Rings

Hopf Algebras and Their Actions on Rings PDF Author: Susan Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821807382
Category : Mathematics
Languages : en
Pages : 258

Book Description
The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

Foundations of Quantum Group Theory

Foundations of Quantum Group Theory PDF Author: Shahn Majid
Publisher: Cambridge University Press
ISBN: 9780521648684
Category : Group theory
Languages : en
Pages : 668

Book Description
A graduate level text which systematically lays out the foundations of Quantum Groups.

Representations of Algebraic Groups

Representations of Algebraic Groups PDF Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594

Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.