On modular invariants of twisted group von Neumann algebras of almost unimodular groups
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917050163658752 |
|---|---|
| author | Guinto, Aldo Garcia Miyamoto, Yuki |
| author_facet | Guinto, Aldo Garcia Miyamoto, Yuki |
| contents | Given a locally compact second countable group $G$ with a 2-cocycle $ω$, we show that the restriction of the twisted Plancherel weight $φ^ω_G$ to the subalgebra generated by a closed subgroup $H$ in the twisted group von Neumann algebra $L_ω(G)$ is semifinite if and only if $H$ is open. When $G$ is almost unimodular, i.e. $\kerΔ_G$ is open, we show that $L_ω(G)$ can be represented as a cocycle action of the $Δ_G(G)$ on $L_ω(\kerΔ_G)$ and the basic construction of the inclusion $L_ω(\kerΔ_G)\leq L_ω(G)$ can be realized as a twisted group von Neumann algebra of $Δ_G(G)\hat{\ } \times G$, where $Δ_G$ is the modular function. Furthermore, when $G$ has a sufficiently large non-unimodular part, we give a characterization of $L_ω(G)$ being a factor and provide a formula for the modular spectrum of $L_ω(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On modular invariants of twisted group von Neumann algebras of almost unimodular groups Guinto, Aldo Garcia Miyamoto, Yuki Operator Algebras Group Theory Given a locally compact second countable group $G$ with a 2-cocycle $ω$, we show that the restriction of the twisted Plancherel weight $φ^ω_G$ to the subalgebra generated by a closed subgroup $H$ in the twisted group von Neumann algebra $L_ω(G)$ is semifinite if and only if $H$ is open. When $G$ is almost unimodular, i.e. $\kerΔ_G$ is open, we show that $L_ω(G)$ can be represented as a cocycle action of the $Δ_G(G)$ on $L_ω(\kerΔ_G)$ and the basic construction of the inclusion $L_ω(\kerΔ_G)\leq L_ω(G)$ can be realized as a twisted group von Neumann algebra of $Δ_G(G)\hat{\ } \times G$, where $Δ_G$ is the modular function. Furthermore, when $G$ has a sufficiently large non-unimodular part, we give a characterization of $L_ω(G)$ being a factor and provide a formula for the modular spectrum of $L_ω(G)$. |
| title | On modular invariants of twisted group von Neumann algebras of almost unimodular groups |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2510.26108 |