definition of $G$-$C^*$ algebra

Question

I wonder what is the precise definition of a $G$-$C^*$ algebra.The document I read gave the definition of $G$-$C^*$ algebras as following:

$C^*$-algebras with a strongly continuous action by automorphisms of the group $G$.Does it mean that $G\times A\to A$ is continuous ? what is the meaning of action of automorphisms of the group?

Answer 1

For $G$ a topological group, a $G$-$C^*$-algebra is a $C^*$-algebra $A$ with an action of $G$ on $A$ by $*$-automorphisms, such that for each $a\in A$, the map $G\to A$ given by $g\mapsto ga$ is continuous (this is so-called strong continuity).