Imprimitivity theorems and self-similar actions on Fell bundles

TL;DR

This paper introduces self-similar actions of groupoids on Fell bundles, leading to a new imprimitivity theorem that generalizes previous results involving group and groupoid actions.

Contribution

It presents a novel framework for self-similar actions on Fell bundles and derives a generalized imprimitivity theorem from these dynamics.

Findings

New notion of self-similar actions on groupoids and Fell bundles

A generalized imprimitivity theorem derived from these actions

Unification of earlier imprimitivity theorems involving groups and groupoids

Abstract

We introduce the notion of self-similar actions of grouopids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and groupoid actions.