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arXiv · 2111.10911

Subproduct systems with quantum group symmetry

Erik Habbestad·Sergey Neshveyev
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Abstract

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.

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Erik Habbestad, Sergey Neshveyev. 2021-11-21. Subproduct systems with quantum group symmetry. https://doi.org/10.4171/jncg%2F523

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