Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces
| dc.creator | Bozejko, Marek | |
| dc.creator | Speicher, Roland | |
| dc.date | 1994-08-30 | |
| dc.date.accessioned | 2026-07-07T09:13:29Z | |
| dc.date.available | 2026-07-07T09:13:29Z | |
| dc.description | In this article we prove that quasi-multiplicative (with respect to the usual length function) mappings on the permutation group $\SSn$ (or, more generally, on arbitrary amenable Coxeter groups), determined by self-adjoint contractions fulfilling the braid or Yang-Baxter relations, are completely positive. We point out the connection of this result with the construction of a Fock representation of the deformed commutation relations $d_id_j^*-\sum_{r,s} t_{js}^{ir} d_r^*d_s=δ_{ij}\id$, where the matrix $t_{js}^{ir}$ is given by a self-adjoint contraction fulfilling the braid relation. Such deformed commutation relations give examples for operator spaces as considered by Effros, Ruan and Pisier. The corresponding von Neumann algebras, generated by $G_i=d_i+d_i^*$, are typically not injective. | |
| dc.description | 26 pages, amstex 3.0 | |
| dc.identifier | https://arxiv.org/abs/funct-an/9408002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9408002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152341 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces | |
| dc.type | text |