An Imprimitivity Theorem for Partial Actions

TL;DR

This paper generalizes Raeburn's Symmetric Imprimitivity Theorem to the setting of partial actions on upper semicontinuous bundles of C*-algebras, introducing new constructions and conditions.

Contribution

It introduces a framework for proper, free, and commuting partial actions on C*-algebra bundles and extends the imprimitivity theorem to this context.

Findings

Constructed the C*-algebra induced by a partial action.

Generalized Raeburn's Symmetric Imprimitivity Theorem to partial actions.

Provided conditions for proper, free, and commuting partial actions.

Abstract

We define proper, free and commuting partial actions on upper semicontinuous bundles of $C^*-$algebras. With such, we construct the $C^*-$algebra induced by a partial action and a partial actions on that algebra. Using those action we give a generalization, to partial actions, of Raeburn's Symmetric Imprimitivity Theorem.