Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces

Details Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces

1994-08-30

arxiv.org/abs/funct-an/9408002v1

Mathematics

Operator Algebras

26 pages, amstex 3.0

Scientific paper

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 $d_id_j^*-\sum_{r,s} t_{js}^{ir} d_r^*d_s=\delta_{ij}\id$, 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.

Affiliated with

Also associated with

No associations

Rating

Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completely Positive Maps on Coxeter Groups, Deformed Commutation Relations, and Operator Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-523311