Enveloping actions for twisted partial actions

TL;DR

This paper generalizes the concept of enveloping actions to twisted partial actions, constructs Morita contexts between partial and global crossed products, and explores conditions for separability of extensions.

Contribution

It introduces a generalized theorem for enveloping actions in twisted partial actions and establishes Morita equivalences with global crossed products.

Findings

Generalized enveloping action existence for twisted partial actions

Constructed Morita context between partial and global crossed products

Analyzed conditions for separable extensions

Abstract

Let A#_{\alpha, \omega}H be a partial crossed product. In this paper, we first generalize the theorem about the existence of an enveloping action to twisted partial actions. Second, we construct a Morita context between the partial crossed product and the crossed product related to the enveloping action. Furthermore, we discuss equivalences of partial crossed products Finally, we investigate when A\subset A#_{\alpha, \omega}H becomes a separable extension.