Lattice extensions of Hecke algebras

JOURNAL OF ALGEBRA

卷:503

Article

Marin, Ivan¹ 

[1] Univ Picardie Jules Verne, UMR CNRS 7352, LAMFA, Amiens, France

关键词: Hecke algebras;    Yokonuma-Hecke algebras;    Complex reflection groups;   

DOI  :  10.1016/j.jalgebra.2018.02.003

来源: Elsevier

【 摘 要 】

We investigate the extensions of the Hecke algebras of finite (complex) reflection groups by lattices of reflection subgroups that we introduced, for some of them, in our previous work on the Yokonuma-Hecke algebras and their connections with Artin groups. When the Hecke algebra is attached to the symmetric group, and the lattice contains all reflection subgroups, then these algebras are the diagram algebras of braids and ties of Aicardi and Juyumaya. We prove a structure theorem for these algebras, generalizing a result of Espinoza and Ryom-Hansen from the case of the symmetric group to the general case. We prove that these algebras are symmetric algebras at least when W is a Coxeter group, and in general under the trace conjecture of Broue, Malle and Michel. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free