Equivariant spectral triple for the quantum group $U_q(2)$ for complex deformation parameters
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911377840406528 |
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| author | Guin, Satyajit Saurabh, Bipul |
| author_facet | Guin, Satyajit Saurabh, Bipul |
| contents | Let $q=|q|e^{iπθ},\,θ\in(-1,1],$ be a nonzero complex number such that $|q|\neq 1$ and consider the compact quantum group $U_q(2)$. For $θ\notin\mathbb{Q}\setminus\{0,1\}$, we obtain the $K$-theory of the $C^*$-algebra $C(U_q(2))$. We construct a spectral triple on $U_q(2)$ which is equivariant under its own comultiplication action. The spectral triple obtained here is even, $4^+$-summable, non-degenerate, and the Dirac operator acts on two copies of the $L^2$-space of $U_q(2)$. The $K$-homology class of the associated Fredholm module is shown to be nontrivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11473 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Equivariant spectral triple for the quantum group $U_q(2)$ for complex deformation parameters Guin, Satyajit Saurabh, Bipul Operator Algebras Quantum Algebra 58B34, 58B32, 46L87 Let $q=|q|e^{iπθ},\,θ\in(-1,1],$ be a nonzero complex number such that $|q|\neq 1$ and consider the compact quantum group $U_q(2)$. For $θ\notin\mathbb{Q}\setminus\{0,1\}$, we obtain the $K$-theory of the $C^*$-algebra $C(U_q(2))$. We construct a spectral triple on $U_q(2)$ which is equivariant under its own comultiplication action. The spectral triple obtained here is even, $4^+$-summable, non-degenerate, and the Dirac operator acts on two copies of the $L^2$-space of $U_q(2)$. The $K$-homology class of the associated Fredholm module is shown to be nontrivial. |
| title | Equivariant spectral triple for the quantum group $U_q(2)$ for complex deformation parameters |
| topic | Operator Algebras Quantum Algebra 58B34, 58B32, 46L87 |
| url | https://arxiv.org/abs/2102.11473 |