1. Hecke-Hopf algebras
- Author
-
David Kazhdan and Arkady Berenstein
- Subjects
Nichols algebra ,Pure mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,010102 general mathematics ,Coxeter group ,Mathematics - Rings and Algebras ,Hopf algebra ,01 natural sciences ,Rings and Algebras (math.RA) ,Symmetric group ,Mathematics::Quantum Algebra ,Mathematics - Quantum Algebra ,FOS: Mathematics ,Quantum Algebra (math.QA) ,Representation Theory (math.RT) ,0101 mathematics ,Mathematics::Representation Theory ,Mathematics - Representation Theory ,Mathematics - Abstract
Let $W$ be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras $H_{\bf q}(W)$ as (left) coideal subalgebras. Our Hecke-Hopf algebras ${\bf H}(W)$ have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of $H_{\bf q}(W)$-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras, for an arbitrary Coxeter group $W$ the "Demazure" part of ${\bf H}(W)$ is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra., Comment: AMSLaTex 67 pages, to appear in Advances in Mathematics
- Published
- 2019