Hopf Algebras and Root Systems

ISBN-13: 9781470452322 / Angielski / Twarda / 2020 / 582 str.

Istvan Heckenberger;Hans-Jurgen Schneider

Spis treści

• Hopf algebras, Nichols algebras, braided monoidal categories, and quantized enveloping algebras: 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, Weyl groupoids, and root systems: Cartan graphs and Weyl groupoids
• The structure of Cartan graphs and root systems
• Cartan graphs of Lie superalgebras
• Weyl groupoids and root systems of Nichols algebras: 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
• Applications: Nichols algebras of diagonal type
• Nichols algebras of Cartan type
• Nichols algebras over non-abelian groups
• Bibliography
• Index of symbols
• Subject index.