Duality of partial Rokhlin dimension

TL;DR

This paper explores the duality relationships between Rokhlin dimension and representability dimension in the context of partial and global actions by finite abelian groups.

Contribution

It introduces a dual representability dimension for global actions and establishes duality results linking partial and global Rokhlin and representability dimensions.

Findings

Rokhlin dimension of a partial action equals the dual representability dimension of the dual action.

Representability dimension of a partial action equals the Rokhlin dimension of its dual.

The paper extends the framework of representability dimension to partial actions.

Abstract

We extend the notion of representability dimension to partial actions and introduce a notion of dual representability dimension for global actions by finite abelian groups. We show that the Rokhlin dimension of a partial action by a finite abelian group agrees with the dual representability dimension of the dual action on the partial crossed product, while the representability dimension of a partial action agrees with the Rokhlin dimension of its dual.