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arXiv · 2212.08512

Subproduct systems with quantum group symmetry. II

Erik Habbestad·Sergey Neshveyev
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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 $U_q(2)$.

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Erik Habbestad, Sergey Neshveyev. 2022-12-16. Subproduct systems with quantum group symmetry. II. https://doi.org/10.1090/tran%2F9459

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