Outer conjugacy of shifts on the hyperfinite II₁-factor

Donald John Charles Bures and Hong Sheng Yin

Vol. 142 (1990), No. 2, 245–257

DOI: 10.2140/pjm.1990.142.245

Abstract

For a shift σ on the hyperfinite II₁ factor R, we define the derived shift σ_∞ to be the restriction of σ to the von Neumann algebra generated by the (σ^k(R))′∩ R. Outer conjugacy of shifts implies conjugacy of derived shifts. In the case of n-shifts with n prime, we calculate σ_∞ explicitly. Combining this with the known classification of n-shifts up to conjugacy, we obtain useful outer-conjugacy invariants for n-shifts.

Mathematical Subject Classification 2000

Primary: 46L55

Milestones

Received: 21 March 1988

Published: 1 April 1990