G-linear map

This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition

Let $G$ be a group, and $(\rho ,V)$ and $(\sigma ,W)$ be representations of $G$. Then a linear map $\varphi :V\to W$ is called G-linear if $\varphi g=g\varphi$ for all $g\in G$.