Quasi-Hopf Algebras
Title | Quasi-Hopf Algebras PDF eBook |
Author | Daniel Bulacu |
Publisher | Cambridge University Press |
Pages | 545 |
Release | 2019-02-21 |
Genre | Mathematics |
ISBN | 1108427014 |
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
Title | Quasi-Hopf Algebras PDF eBook |
Author | Daniel Bulacu |
Publisher | Cambridge University Press |
Pages | 546 |
Release | 2019-02-21 |
Genre | Mathematics |
ISBN | 1108632653 |
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.
Hopf Algebras and Generalizations
Title | Hopf Algebras and Generalizations PDF eBook |
Author | Louis H. Kauffman |
Publisher | American Mathematical Soc. |
Pages | 186 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821838202 |
Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.
Hopf Algebras and Quantum Groups
Title | Hopf Algebras and Quantum Groups PDF eBook |
Author | Stefaan Caenepeel |
Publisher | CRC Press |
Pages | 332 |
Release | 2000-04-05 |
Genre | Science |
ISBN | 9780824703950 |
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.
Hopf Algebras in Noncommutative Geometry and Physics
Title | Hopf Algebras in Noncommutative Geometry and Physics PDF eBook |
Author | Stefaan Caenepeel |
Publisher | CRC Press |
Pages | 344 |
Release | 2019-05-07 |
Genre | Mathematics |
ISBN | 1482276712 |
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Hopf Algebras, Tensor Categories and Related Topics
Title | Hopf Algebras, Tensor Categories and Related Topics PDF eBook |
Author | Nicolás Andruskiewitsch |
Publisher | American Mathematical Soc. |
Pages | 359 |
Release | 2021-07-06 |
Genre | Education |
ISBN | 1470456249 |
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.
Classical Hopf Algebras and Their Applications
Title | Classical Hopf Algebras and Their Applications PDF eBook |
Author | Pierre Cartier |
Publisher | Springer Nature |
Pages | 277 |
Release | 2021-09-20 |
Genre | Mathematics |
ISBN | 3030778452 |
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.