Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916207106457600 |
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| author | Kaluba, Marek Mizerka, Piotr Nowak, Piotr W. |
| author_facet | Kaluba, Marek Mizerka, Piotr Nowak, Piotr W. |
| contents | We show that the cohomological Laplacian in degree 1 in the group cohomology of $\operatorname{SL}_3(\mathbb{Z})$ is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb{R}G)$. We provide an estimate of the spectral gap for this Laplacian for every unitary representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_02783 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$ Kaluba, Marek Mizerka, Piotr Nowak, Piotr W. Group Theory Operator Algebras We show that the cohomological Laplacian in degree 1 in the group cohomology of $\operatorname{SL}_3(\mathbb{Z})$ is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb{R}G)$. We provide an estimate of the spectral gap for this Laplacian for every unitary representation. |
| title | Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$ |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2207.02783 |