Enveloping actions and duality theorems for partial twisted smash products

TL;DR

This paper extends the theory of partial twisted smash products by establishing enveloping actions, Morita contexts, and duality theorems, thereby broadening the understanding of their algebraic structure and relationships.

Contribution

It generalizes the existence of enveloping actions to partial twisted smash products and constructs Morita contexts, linking partial and global twisted smash products.

Findings

Generalized enveloping action existence for partial twisted smash products

Constructed Morita context between partial and global twisted smash products

Extended duality theorems to partial twisted smash products

Abstract

In this paper, we first generalize the theorem about the existence of an enveloping action to a partial twisted smash product. Second, we construct a Morita context between the partial twisted smash product and the twisted smash product related to the enveloping action. Furthermore, we show some results relating partial actions and partial representations over the partial twisted smash products, which generalize the results of Alves and Batista (Comm. Algebra, 38(8): 2872-2902, 2010). Finally, we present versions of the duality theorems of Blattner-Montgomery for partial twisted smash products.