Hopf Algebras and Root Systems - 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 Root Systems write by István Heckenberger. This book was released on 2020-06-19. Hopf Algebras and Root Systems available in PDF, EPUB and Kindle. 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.
Algebras, Rings and Modules
Algebras, Rings and Modules - 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 Algebras, Rings and Modules write by Michiel Hazewinkel. This book was released on 2010. Algebras, Rings and Modules available in PDF, EPUB and Kindle. 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 chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.
Advances in Hopf Algebras
Advances in 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 Advances in Hopf Algebras write by Jeffrey Bergen. This book was released on 1994-04-19. Advances in Hopf Algebras available in PDF, EPUB and Kindle. "This remarkable reference covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras. "
New Directions in Hopf Algebras
New Directions in 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 New Directions in Hopf Algebras write by Susan Montgomery. This book was released on 2002-05-06. New Directions in Hopf Algebras available in PDF, EPUB and Kindle. Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.
Hopf Algebras
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 Hopf Algebras write by David E. Radford. This book was released on 2011. Hopf Algebras available in PDF, EPUB and Kindle. 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.
