Cohomology of actions of discrete groups on factors of type II₁

Yasuyuki Kawahigashi

Vol. 149 (1991), No. 2, 303–317

DOI: 10.2140/pjm.1991.149.303

Abstract

We study 1-cohomology of discrete group actions on factors of type II₁. Characterizations of Kazhdan’s property T and amenability for discrete groups in terms of cocycles and coboundaries are given, and we show that each of SL(n,Z), n ≥ 3, and Sp(n,Z), n ≥ 2, has a continuous family of mutually non-cocycle conjugate free actions on the AFD factor of type II₁ as an application. We also introduce and compute entropy for discrete amenable group action on factors of type II₁.

Mathematical Subject Classification 2000

Primary: 46L55

Secondary: 46L37, 46L40

Milestones

Received: 4 January 1990

Published: 1 June 1991