$\mathrm{SL}_{4}(\mathbf{Z})$ is not purely matricial field
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915213419216896 |
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| author | Magee, Michael de la Salle, Mikael |
| author_facet | Magee, Michael de la Salle, Mikael |
| contents | We prove that every finite dimensional unitary representation of $\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero $\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector. As a consequence, there is no sequence of finite-dimensional representations of $\mathrm{SL}_{4}(\mathbf{Z})$ that gives rise to an embedding of its reduced $C^*$-algebra into an ultraproduct of matrix algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03220 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $\mathrm{SL}_{4}(\mathbf{Z})$ is not purely matricial field Magee, Michael de la Salle, Mikael Group Theory Operator Algebras We prove that every finite dimensional unitary representation of $\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero $\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector. As a consequence, there is no sequence of finite-dimensional representations of $\mathrm{SL}_{4}(\mathbf{Z})$ that gives rise to an embedding of its reduced $C^*$-algebra into an ultraproduct of matrix algebras. |
| title | $\mathrm{SL}_{4}(\mathbf{Z})$ is not purely matricial field |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2312.03220 |