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Hopf Algebras and Root Systems (Hardcover)
Loot Price: R3,522
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Hopf Algebras and Root Systems (Hardcover)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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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.
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