Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart: "Gradings by root systems and S-structures on Lie algebras"
Presenter
May 1, 2024
Keywords:
- key words Lie algebras
- Representation theory
- combinatorics
MSC:
- 05-XX - Combinatorics {For finite fields
- see 11Txx}
- 16-XX - Associative rings and algebras {For the commutative case
- see 13-XX}
- 17-XX - Nonassociative rings and algebras
- 20-XX - Group theory and generalizations
Abstract
Gradings by root systems of Lie algebras is an area where the contributions of Georgia Benkart are of fundamental importance. A few years ago, Vinberg considered a broad extension. In this talk the S-structures of Vinberg will be reviewed, examples that had already appeared in the literature and that fit in this framework will be given, and some new examples, obtained in joint work with P. Beites, A. Córdova-Martínez, and I. Cunha, will be provided.