Envolventes para ações parciais de grupos e de álgebras de Hopf

Abstract

Based on the articles Associativity of crossed produts by partial actions, enveloping actions and partial representations" of M. Dokuchaev and R. Exel ([7] and Enveloping Actions for Partial Hopf Actions" of M.M.S. Alves and E. Batista ([3]), we will report conditions for the existence of enveloping actions of partial group actions and partial Hopf algebra actions. The main results are: 1. Every partial action {αg:Dg−1→Dg:g∈G} of a group G on an unital associative algebra admits only one enveloping action if and only if, the ideals Dg are unital algebras; 2. Every left partial action of a Hopf algebra H on an unital associative algebra admits an enveloping action. Moreover, every left partial Hopf action is equivalent to a left partial action induced by the enveloping action; 3. Two miminal enveloping actions of a parcial Hopf action are isomorphic as left H-module algebras.