Groups with compact open subgroups and multiplier Hopf $^*$-algebras
| dc.creator | Landstad, Magnus B. | |
| dc.creator | Van Daele, A. | |
| dc.date | 2007-01-19 | |
| dc.date | 2007-10-02 | |
| dc.date.accessioned | 2026-07-07T08:33:23Z | |
| dc.date.available | 2026-07-07T08:33:23Z | |
| dc.description | For a locally compact group $G$ we look at the group algebras $C_0(G)$ and $C_r^*(G)$, and we let $f\in C_0(G)$ act on $L^2(G)$ by the multiplication operator $M(f)$. We show among other things that the following properties are equivalent: 1. $G$ has a compact open subgroup. 2. One of the $C^*$-algebras has a dense multiplier Hopf $^*$-subalgebra (which turns out to be unique). 3. There are non-zero elements $a\in C_r^*(G)$ and $f\in C_0(G)$ such that $aM(f)$ has finite rank. 4. There are non-zero elements $a\in C_r^*(G)$ and $f\in C_0(G)$ such that $aM(f)=M(f)a$. If $G$ is abelian, these properties are equivalent to: 5. There is a non-zero continuous function with the property that both $f$ and $\hat f$ have compact support. | |
| dc.description | 23 pages. Section 1 has been shortened and improved. To appear in Expositiones Mathematicae | |
| dc.identifier | https://arxiv.org/abs/math/0701525 | |
| dc.identifier | http://arxiv.org/abs/math/0701525 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139113 | |
| dc.subject | Operator Algebras | |
| dc.subject | 22D15; 46L05 | |
| dc.title | Groups with compact open subgroups and multiplier Hopf $^*$-algebras | |
| dc.type | text |