A study of nil Hecke algebras via Hopf algebroids
Representation Theory
2024-10-16 v3 Combinatorics
Quantum Algebra
Rings and Algebras
Abstract
Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without an antipode. The proof relies on mixed dihedral braid relations between Demazure operators and simple reflections. For researchers new to Hopf algebroids we include additional examples from ring theory, representation theory, and algebraic geometry.
Cite
@article{arxiv.2410.08061,
title = {A study of nil Hecke algebras via Hopf algebroids},
author = {Zbigniew Wojciechowski},
journal= {arXiv preprint arXiv:2410.08061},
year = {2024}
}