Classification of Invariant Subalgebras in a class of factors with property (T)
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915719899250688 |
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| author | Jiang, Yongle Li, Hongyi |
| author_facet | Jiang, Yongle Li, Hongyi |
| contents | Let $n\geq 2$ and $G_n=\mathbb{Z}^n\rtimes SL_n(\mathbb{Z})$. We classify all $G_n$-invariant von Neumann subalgebras in $L(G_n)$. For $n=2$, this gives an alternative proof of the previous result of Jiang-Liu. For $n\geq 3$, this gives the first class of property (T) groups without the invariant subalgebras rigidity property but invariant subalgebras in the corresponding group factors can still be classified. As a corollary, $L(G_n)$ admits a unique maximal Haagerup $G_n$-invariant von Neumann subalgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06353 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of Invariant Subalgebras in a class of factors with property (T) Jiang, Yongle Li, Hongyi Operator Algebras 46L10, 22D55, 47C15 Let $n\geq 2$ and $G_n=\mathbb{Z}^n\rtimes SL_n(\mathbb{Z})$. We classify all $G_n$-invariant von Neumann subalgebras in $L(G_n)$. For $n=2$, this gives an alternative proof of the previous result of Jiang-Liu. For $n\geq 3$, this gives the first class of property (T) groups without the invariant subalgebras rigidity property but invariant subalgebras in the corresponding group factors can still be classified. As a corollary, $L(G_n)$ admits a unique maximal Haagerup $G_n$-invariant von Neumann subalgebra. |
| title | Classification of Invariant Subalgebras in a class of factors with property (T) |
| topic | Operator Algebras 46L10, 22D55, 47C15 |
| url | https://arxiv.org/abs/2601.06353 |