Hopf algebras and root systems

Hopf algebras and root systems / István Heckenberger, Hans-Jürgen Schneider.

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 relation...

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Bibliographic Details
Main Authors: Heckenberger, István, 1969- (Author), Schneider, Hans-Jürgen, 1944- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2020]
Series:Mathematical surveys and monographs ; no. 247.
Subjects:
Hopf algebras.
Root systems (Algebra)
Weyl groups.
Table of Contents:
  • A quick introduction to Nichols algebras
  • Basic Hopf algebra theory
  • Braided monoidal categories
  • Yetter-Drinfeld modules over Hopf algebras
  • Gradings and filtrations
  • Braided structures
  • Nichols algebras
  • Quantized enveloping algebras and generalizations
  • Cartan graphs and Weyl groupoids
  • The structure of Cartan graphs and root systems
  • Cartan graphs of Lie superalgebras
  • A braided monoidal isomorphism of Yetter-Drinfeld modules
  • Nichols systems, and semi-Cartan graph of Nichols algebras
  • Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras
  • Nichols algebras of diagonal type
  • Nichols algebras of Cartan type
  • Nichols algebras over non-abelian groups.

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