Heckenberger, Istvan Schneider, Hans-jurgen Hopf algebras and root systems 9781470452322

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Автор: Heckenberger, Istvan Schneider, Hans-jurgen
Название: Hopf algebras and root systems
ISBN: 9781470452322
Издательство: Mare Nostrum (Eurospan)
Классификация:

Алгебра

Геометрия

Алгебраическая геометрия

ISBN-10: 1470452324
Обложка/Формат: Hardback
Страницы: 582
Вес: 1.24 кг.
Дата издания: 30.08.2020
Серия: Mathematical surveys and monographs
Язык: English
Размер: 210 x 235 x 11
Ключевые слова: Algebra,Algebraic geometry
Рейтинг:
Поставляется из: Англии
Описание: 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.
Дополнительное описание: Algebra|Algebraic geometry

Hopf algebras and root systems, Heckenberger, Istvan Schneider, Hans-jurgen