Hecke algebras from groups acting on trees and HNN extensions

Baumgartner, Udo and Laca, Marcelo and Ramagge, Jacqui and Willis, George (2009) Hecke algebras from groups acting on trees and HNN extensions. Journal of Algebra, 321 (11). pp. 3065-3088.

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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.

Item Type: Article
Uncontrolled Keywords: Hecke algebras, trees, C*-algebras, topological groups, HNN extensions
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05

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