Groupoid approach to the dynamical system of commutative von Neumann Algebras

Abstract

The automorphism group $Aut(X,\mu )$ of a compact, complete metric space $X$ with a Radon measure $\mu$ is a subgroup of $\mathcal{U}(L^2(X,\mu ))$-the unitary group of operators on $L^2(X,\mu )$. The $Aut(X,\mu )$-action on the generalized space $\mathcal{M}(X)$ is a proper action. Hence, there exists a slice at each point of the generalized space $\mathcal{M}(X)$. Measure Groupoid (virtual group) is subsequently employed to analyze the resulting dynamical system as that of the ergodic action of the commutative algebra (a lattice) $C(X)$ on the generalized space $\mathcal{M}(X)$ which is represented on a commutative von Neumann algebra.

36. arXiv admin note: substantial text overlap with arXiv:2101.08159

References in corpus (1)

• Polar manifolds and actions