dorsal/arxiv
View SchemaNon-commutative Factor theorem for tensor products of lattices in product groups
| Authors | Tattwamasi Amrutam, Yongle Jiang, Shuoxing Zhou |
|---|---|
| Categories | |
| ArXiv ID | 2601.09875vv1 |
| URL | https://arxiv.org/abs/2601.09875 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\Gamma < G= G_1 \times \dots \times G_d$ in higher rank semisimple algebraic groups and a trace-preserving irreducible action $G \curvearrowright (\mathcal{N}, \tau)$, we show that every intermediate von Neumann algebra between $\mathcal{N}\rtimes\Gamma$ and $(L^\infty(G/P,\nu_P)\overline{\otimes}\mathcal{N})\rtimes\Gamma$ is again a crossed product of the form $(L^\infty(G/Q,\nu_Q)\overline{\otimes}\mathcal{N})\rtimes\Gamma$.
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"date_created": "2026-02-17T05:53:23.750000Z",
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"abstract": "We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\\Gamma \u003c G= G_1 \\times \\dots \\times G_d$ in higher rank semisimple algebraic groups and a trace-preserving irreducible action $G \\curvearrowright (\\mathcal{N}, \\tau)$, we show that every intermediate von Neumann algebra between $\\mathcal{N}\\rtimes\\Gamma$ and $(L^\\infty(G/P,\\nu_P)\\overline{\\otimes}\\mathcal{N})\\rtimes\\Gamma$ is again a crossed product of the form $(L^\\infty(G/Q,\\nu_Q)\\overline{\\otimes}\\mathcal{N})\\rtimes\\Gamma$.",
"arxiv_id": "2601.09875",
"authors": [
"Tattwamasi Amrutam",
"Yongle Jiang",
"Shuoxing Zhou"
],
"categories": [
"math.OA",
"math.DS",
"math.FA"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Non-commutative Factor theorem for tensor products of lattices in product groups",
"url": "https://arxiv.org/abs/2601.09875",
"version": "v1"
},
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"source": {
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