https://u-picardie.hal.science/hal-03621314Marin, IvanIvanMarinLAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 - UPJV - Université de Picardie Jules Verne - CNRS - Centre National de la Recherche ScientifiqueLattice extensions of Hecke algebrasHAL CCSD2018[MATH] Mathematics [math]DESSAIVRE, Louise2022-03-28 10:19:212023-03-24 14:53:262022-03-28 10:19:21enJournal articles10.1016/j.jalgebra.2018.02.0031We 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.