Generalised Hecke algebras and C^*-completions
| dc.creator | Landstad, Magnus B. | |
| dc.creator | Larsen, Nadia S. | |
| dc.date | 2006-09-14 | |
| dc.date | 2007-10-03 | |
| dc.date.accessioned | 2026-07-07T08:33:38Z | |
| dc.date.available | 2026-07-07T08:33:38Z | |
| dc.description | For a Hecke pair $(G, H)$ and a finite-dimensional representation $σ$ of $H$ on $V_σ$ with finite range we consider a generalised Hecke algebra $\H_σ(G, H)$, which we study by embedding the given Hecke pair in a Schlichting completion $(G_σ, H_σ)$ that comes equipped with a continuous extension $σ$ of $H_σ$. There is a (non-full) projection $p_σ\in C_c(G_σ, {\cc B}(V_σ))$ such that $\H_σ(G, H)$ is isomorphic to $p_σC_c(G_σ, {\cc B}(V_σ))p_σ$. We study the structure and properties of $C^*$-completions of the generalised Hecke algebra arising from this corner realisation, and via Morita-Fell-Rieffel equivalence we identify, in some cases explicitly, the resulting proper ideals of $C^*(G_σ, {\cc B}(V_σ))$. By letting $σ$ vary, we can compare these ideals. The main focus is on the case with $\dimσ=1$ and applications include $ax+b$-groups and the Heisenberg group. | |
| dc.description | 25 pages. Revised version | |
| dc.identifier | https://arxiv.org/abs/math/0609386 | |
| dc.identifier | http://arxiv.org/abs/math/0609386 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139198 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55; 20C08 | |
| dc.title | Generalised Hecke algebras and C^*-completions | |
| dc.type | text |