Pseudo-Riemannian Spectral Triples for $\mathrm{SU}(1,1)$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915761897865216 |
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| author | de Groot, Jort |
| author_facet | de Groot, Jort |
| contents | We use the harmonic analysis of $\mathrm{SU}(1,1)$ to show that the triple $(\mathcal{A},\mathcal{H},D)$, with $D$ (the closure of) Kostant's cubic Dirac operator acting on the Hilbert space $\mathcal{H}=L^2(\mathrm{SU}(1,1))\otimes\mathbb{C}^2$, and with $*$-algebra $\mathcal{A}=C^\infty_c(\mathrm{SU}(1,1))\otimes 1$, forms both a pseudo-Riemannian spectral triple in the sense of Van den Dungen, Paschke and Rennie, and an indefinite spectral triple in the sense of Van den Dungen and Rennie. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-Riemannian Spectral Triples for $\mathrm{SU}(1,1)$ de Groot, Jort Differential Geometry Operator Algebras Representation Theory We use the harmonic analysis of $\mathrm{SU}(1,1)$ to show that the triple $(\mathcal{A},\mathcal{H},D)$, with $D$ (the closure of) Kostant's cubic Dirac operator acting on the Hilbert space $\mathcal{H}=L^2(\mathrm{SU}(1,1))\otimes\mathbb{C}^2$, and with $*$-algebra $\mathcal{A}=C^\infty_c(\mathrm{SU}(1,1))\otimes 1$, forms both a pseudo-Riemannian spectral triple in the sense of Van den Dungen, Paschke and Rennie, and an indefinite spectral triple in the sense of Van den Dungen and Rennie. |
| title | Pseudo-Riemannian Spectral Triples for $\mathrm{SU}(1,1)$ |
| topic | Differential Geometry Operator Algebras Representation Theory |
| url | https://arxiv.org/abs/2601.22171 |