Subproduct systems with quantum group symmetry. II

Abstract

We complete our analysis of the Temperley-Lieb subproduct systems, which define quantum analogues of Arveson's $2$-shift, by extending the main results of the previous paper to the general parameter case. Specifically, we show that the associated Toeplitz algebras are nuclear, find complete sets of relations for them, prove that they are equivariantly $KK$-equivalent to $\mathbb{C}$ and compute the $K$-theory of the associated Cuntz-Pimsner algebras. A key role is played by quantum symmetry groups, first studied by Mrozinski, preserving Temperley-Lieb polynomials up to rescaling, and their monoidal equivalence to $U_q(2)$.

23 pages; v2: minor corrections, revised preliminary section

References in corpus (6)

• Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups
• The Baum-Connes conjecture for free orthogonal quantum groups
• A Remark on Quantum Group Actions and Nuclearity
• Braided quantum SU(2) groups
• Gysin sequences and SU(2)-symmetries of C*-algebras
• Subproduct systems with quantum group symmetry