2021/11/21 by Habbestad, Erik, Neshveyev, Sergey · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2111.10911
We introduce a class of subproduct systems of finite dimensional Hilbert spaces whose fibers are defined by the Jones-Wenzl projections in Temperley-Lieb algebras. The quantum symmetries of a subclass of these systems are the free orthogonal quantum groups. For this subclass, we show that the corresponding Toeplitz algebras are nuclear C^*-algebras that are KK-equivalent to \mathbb C and obtain a complete list of generators and relations for them. We also show that their gauge-invariant subalgebras coincide with the algebras of functions on the end compactifications of the duals of the free orthogonal quantum groups. Along the way we prove a few general results on equivariant subproduct systems, in particular, on the behavior of the Toeplitz and Cuntz-Pimsner algebras under monoidal equivalence of quantum symmetry groups.