Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory
type: Item
instance of: scholarly article
title: Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory
zbMATH Open document ID: 1056.46061
author: Erling Størmer
author: Sergey Neshveyev
publication date: 2003-11-10T00:00:00Z
review text: If \(T\) is a free ergodic measure preserving action of a countable discrete abelian group \(G\) on a Lebesgue probability space \((X,\mu)\), then the crossed product of \(L^\infty(X)\) by this action contains the two maximal abelian subalgebras \(L^\infty(X)\) and \(G''\). The authors show that if an isomorphism between crossed products respects these subalgebras, then also the underlying groups and measure spaces are isomorphic. Then they weaken the assumptions on the isomorphism. As an application, they show partial results towards the conjecture that the Connes-Størmer entropy of a single ergodic automorphism of the hyperfinite II\(_1\)-factor is determined by the conjugacy class of its group action.
reviewed by: Michael Skeide
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 2002331
zbMATH Keywords: crossed products
zbMATH Keywords: free ergodic measure preserving action
MaRDI profile type: Publication
full work available at URL: s10114-003-0274-2
OpenAlex ID: W1973628491
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DOI: 10.1007/S10114-003-0274-2
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2002331