Partial actions of finite groups- decomposability and Rokhlin theory.

Shirly Geffen (Ben-Gurion University of the Negev)

Thursday 26th November, 2020 16:00-17:00 Contact the organisers for Zoom info

Abstract

The principle topic in this talk is C*-algebraic partial actions. A wide class of well-known C*-algebras can be naturally written as crossed-products by partial actions.
We introduce and study a property, called "the decomposition property", for C*-algebraic partial actions by discrete groups (we will focus on finite groups in this talk). Partial actions with this property ("decomposable partial actions") behave in many ways like global actions, which makes their study particularly accessible. 
We show that decomposable partial actions appear naturally in practice. For example, every partial action by a finite group is an iterated extension of decomposable partial actions.
Using this, we derive a full description of crossed products by partially acting finite groups in terms of global systems.
We develop the concept of Rokhlin dimension for finite group partial actions and show that the expected permanence properties hold. For example, we use decomposability techniques in order to show that finite nuclear dimension is preserved under the formation of crossed products by finite group partial actions with finite Rokhlin dimension.

Joint work with Fernando Abadie and Eusebio Gardella.

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