Property (T) and the Furstenberg Entropy of Nonsingular Actions

Abstract

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure $\mu$ on a countable group $G$, A. Nevo showed that a necessary condition for $G$ to have property (T) is that the Furstenberg $\mu$-entropy values of the ergodic, properly nonsingular $G$-actions are bounded away from zero. We show that this is also a sufficient condition.

10 pages

References in corpus (1)

• Noncommutative real algebraic geometry of Kazhdan's property (T)

Cited by in corpus (2)

• Kudo-Continuity Of Entropy Functionals
• Hypertrace and entropy gap characterizations of property (T) for ${\mathrm{II}}_1$ factors