Groupoid approach to the dynamical system of commutative von Neumann Algebras

2021/01/23 by Okeke, N. O., Egwe, M. E.
#22A22 #37A05 #37A25 #37C80 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2101.11106

Abstract

The automorphism group Aut(X,μ) of a compact, complete metric space X with a Radon measure μ is a subgroup of U(L²(X,μ))-the unitary group of operators on L²(X,μ). The Aut(X,μ)-action on the generalized space M(X) is a proper action. Hence, there exists a slice at each point of the generalized space 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 M(X) which is represented on a commutative von Neumann algebra.

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