A study of nil Hecke algebras via Hopf algebroid theory

arXiv:2410.08061v1 Announce Type: cross
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 a into 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 several additional examples from ring theory, representation theory and algebraic geometry.