Completely positive multipliers of quantum groups

Details Completely positive multipliers of quantum groups Completely positive multipliers of quantum groups

2011-07-26

arxiv.org/abs/1107.5244v3

Mathematics

Operator Algebras

23 pages; some minor tweaks; submitted

Scientific paper

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group $\G$ (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a coisometric corepresentation of $\G$. In the locally compact quantum group case the corepresentation we construct is always unitary, and it follows that there is an order bijection between the completely positive multipliers of $L^1(\G)$ and the positive functionals on the universal quantum group $C_0^u(\G)$. We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak$^*$-weak$^*$-continuous. We also show that for any $\G$, for a completely positive multiplier, our constructed corepresentation can be chosen to be unitary if and only if the left multiplier comes from a double multiplier.

Affiliated with

Also associated with

No associations

Rating

Completely positive multipliers of quantum groups 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 multipliers of quantum groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completely positive multipliers of quantum groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-93965