Hopf Algebras and Root Systems

Hopf Algebras and Root Systems
Author :
Publisher : American Mathematical Soc.
Total Pages : 606
Release :
ISBN-10 : 9781470452322
ISBN-13 : 1470452324
Rating : 4/5 (22 Downloads)

Book Synopsis Hopf Algebras and Root Systems by : István Heckenberger

Download or read book Hopf Algebras and Root Systems written by István Heckenberger and published by American Mathematical Soc.. This book was released on 2020-06-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.


Hopf Algebras and Root Systems Related Books

Hopf Algebras and Root Systems
Language: en
Pages: 606
Authors: István Heckenberger
Categories: Education
Type: BOOK - Published: 2020-06-19 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is
Groups, Rings, Lie and Hopf Algebras
Language: en
Pages: 266
Authors:
Categories: Mathematics
Type: BOOK - Published: 2003-03-31 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Alge
New Directions in Hopf Algebras
Language: en
Pages: 502
Authors: Susan Montgomery
Categories: Mathematics
Type: BOOK - Published: 2002-05-06 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. T
Algebras, Rings and Modules
Language: en
Pages: 425
Authors: Michiel Hazewinkel
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a c
Finite Dimensional Algebras and Quantum Groups
Language: en
Pages: 790
Authors: Bangming Deng
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more striki