Some representations of the automorphism group of an infinite continuous homogeneous measure algebra

Arthur Larry Lieberman

Vol. 44 (1973), No. 2, 607–612

DOI: 10.2140/pjm.1973.44.607

Abstract

Let (X,τ,m) be an infinite continuous homogeneous measure space. Let A be the measure algebra of (X,τ,m) and G be the automorphism group of A. The canonical representation of G on the subspace of all elements of ⊗ⁿL²(X,τ,m) of some fixed maximal symmetry type is irreducible. Two such representations are equivalent iff they correspond to the same n ∈ N and to the same partition of n.

Mathematical Subject Classification 2000

Primary: 22D99

Milestones

Received: 19 April 1971

Published: 1 February 1973