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Hopf Algebras and Root Systems
About this Title
István Heckenberger, Philipps Universität Marburg, Marburg, Germany and Hans-Jürgen Schneider, Ludwig-Maximilians-Universität München, München, Germany
Publication: Mathematical Surveys and Monographs
Publication Year:
2020; Volume 247
ISBNs: 978-1-4704-5232-2 (print); 978-1-4704-5680-1 (online)
DOI: https://doi.org/10.1090/surv/247
MathSciNet review: 4164719
MSC: Primary 16T05; Secondary 16Txx, 17B22
Table of Contents
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Front/Back Matter
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
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