Quantum Symmetries and Strong Haagerup Inequalities

Mathematics – Operator Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Quantum Symmetries and Strong Haagerup Inequalities 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 Quantum Symmetries and Strong Haagerup Inequalities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Symmetries and Strong Haagerup Inequalities will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-400311

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.