Alternating subalgebras of Hecke algebras and alternating subgroups of braid groups

TL;DR

This paper introduces new algebraic structures called alternating subalgebras of Hecke algebras and alternating subgroups of braid groups, providing multiple presentations that generalize classical Coxeter group results.

Contribution

It defines and presents two new algebraic structures related to Coxeter systems, extending classical results with generalized and edge-based presentations.

Findings

Provides two presentations for H^+(G) and B^+(G)

Generalizes Bourbaki's presentation for Coxeter group subgroups

Connects algebraic structures to Coxeter graph edges

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.