Discrete measured groupoid von Neumann algebras via the Gaussian deformation
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_ | 1866915501391740928 |
|---|---|
| author | Flores, Felipe Harbour, James |
| author_facet | Flores, Felipe Harbour, James |
| contents | Given a discrete measured groupoid $\mathcal{G}$, we study properties of the corresponding von Neumann algebra $L(\mathcal{G})$ using the techniques of Popa's deformation/rigidity theory. More specifically, we define and study the Gaussian deformation associated with any $1$-cocycle of $\mathcal{G}$ and use it to prove primeness and fullness under appropriate assumptions. We also characterize the maximal rigid subalgebras of $L(\mathcal{G})$ and produce unique prime factorization results for algebras of the form $L(\mathcal{G}_1\times\ldots\times\mathcal{G}_n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete measured groupoid von Neumann algebras via the Gaussian deformation Flores, Felipe Harbour, James Operator Algebras Dynamical Systems Functional Analysis Primary 46L10, Secondary 37A20, 47L65 Given a discrete measured groupoid $\mathcal{G}$, we study properties of the corresponding von Neumann algebra $L(\mathcal{G})$ using the techniques of Popa's deformation/rigidity theory. More specifically, we define and study the Gaussian deformation associated with any $1$-cocycle of $\mathcal{G}$ and use it to prove primeness and fullness under appropriate assumptions. We also characterize the maximal rigid subalgebras of $L(\mathcal{G})$ and produce unique prime factorization results for algebras of the form $L(\mathcal{G}_1\times\ldots\times\mathcal{G}_n)$. |
| title | Discrete measured groupoid von Neumann algebras via the Gaussian deformation |
| topic | Operator Algebras Dynamical Systems Functional Analysis Primary 46L10, Secondary 37A20, 47L65 |
| url | https://arxiv.org/abs/2509.15161 |