Nuclear dimension of crossed products associated to partial dynamical systems

Abstract

We bound the nuclear dimension of crossed products associated to some partial actions of finite groups or $\mathbb{Z}$ on finite dimensional locally compact Hausdorff second countable spaces. Our results apply to globalizable partial actions, finite group partial actions, minimal partial automorphisms, and partial automorphisms acting on zero-dimensional spaces, or a class of one dimensional spaces, containing $1$-dimensional CW complexes. This extends work on global systems by Hirshberg and Wu.

25 pages, 1 figure. To appear in J. Funct. Anal. Minor changes, accepted version

References in corpus (3)

• A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one
• Decomposable partial actions
• A classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras, I: $C^{\ast }$-algebras with generalized tracial rank one

Cited by in corpus (2)

• Decomposable partial actions
• Partial C*-dynamics and Rokhlin dimension