Subproduct systems with quantum group symmetry. II
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909620410253312 |
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| author | Habbestad, Erik Neshveyev, Sergey |
| author_facet | Habbestad, Erik Neshveyev, Sergey |
| contents | 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 $U_q(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08512 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Subproduct systems with quantum group symmetry. II Habbestad, Erik Neshveyev, Sergey Operator Algebras Quantum Algebra 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 $U_q(2)$. |
| title | Subproduct systems with quantum group symmetry. II |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2212.08512 |