Discrete measured groupoid von Neumann algebras via the Gaussian deformation

Felipe Flores; James Harbour

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arXiv · 2509.15161

Discrete measured groupoid von Neumann algebras via the Gaussian deformation

Felipe Flores·James Harbour

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Abstract

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 $L(\mathcal{G}_1\times\ldots\times\mathcal{G}_n)$.

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BibTeX RIS

Felipe Flores, James Harbour. 2025-09-18. Discrete measured groupoid von Neumann algebras via the Gaussian deformation. https://arxiv.org/abs/2509.15161

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