Hecke algebras from groups acting on trees and HNN extensions

Title: Hecke algebras from groups acting on trees and HNN extensions
Creator: Baumgartner, Udo; Laca, Marcelo; Ramagge, Jacqui; Willis, George
Relation: Journal of Algebra Vol. 321, Issue 11, p. 3065-3088
Publisher Link: http://dx.doi.org/10.1016/j.jalgebra.2008.12.008
Publisher: Elsevier
Resource Type: journal article
Date: 2009
Description: We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and the stabilizer of an end relative to a vertex stabilizer, assuming that the actions are sufficiently transitive. We focus on identifying the structure of the resulting Hecke algebras, give explicit multiplication tables of the canonical generators and determine whether the Hecke algebra has a universal C*-completion. The paper unifies algebraic and analytic approaches by focusing on the common geometric thread. The results have implications for the general theory of totally disconnected locally compact groups.
Subject: Hecke algebras; trees; C*-algebras; topological groups; HNN extensions
Identifier: uon:8055
Identifier: http://hdl.handle.net/1959.13/916622
Identifier: ISSN:0021-8693
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