Definition 9.1.12 (Left and Right Translations).label Let $G$ be a group, $g \in G$, and $Y$ be a set, then
\[L_{g}: Y^{G} \to Y^{G} \quad (L_{g}f)(h) = f(g^{-1}h)\]
is the left translation map by $g$, and
\[R_{g}: Y^{G} \to Y^{G} \quad (R_{g}f)(h) = f(hg)\]
is the right translation map by $g$.
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