Alternating Subalgebras of Hecke Algebras and Alternating Subgroups of Braid Groups

Abstract

For a Coxeter system (G, S) the multi-parametric alternating subalgebra H +(G) of the Hecke algebra and the alternating subgroup ℬ+(G) of the braid group are defined. Two presentations for H +(G) and ℬ+(G) are given; one generalizes the Bourbaki presentation for the alternating subgroups of Coxeter groups, another one uses generators related to edges of the Coxeter graph.