Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory (Q1412953)

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.