Meaning of pre-superscript in group theory

Is pre-superscript a standard notation for something? I've encountered it in the following:

$$(a,g)(b,h) = (a + {}^gb + f(g,h), gh).$$

This was given in relation to a formula for the multiplication on the abelian set $$A$$ with extension $$G$$ as $$A$$ X $$G$$.

• may be conjugation – J. W. Tanner Nov 11 '19 at 2:11
• – J. W. Tanner Nov 11 '19 at 2:18

$${}^g b$$ is, in general, shortand for $$g$$ acting on $$b$$ from the left. Often, this means the left conjugation action $$gbg^{-1}$$ (as opposed to $$b^g = g^{-1} bg$$, the right conjugation action). If $$G$$ and $$A$$ are separate groups, though, and $$G$$ has a distinguished action on $$A$$, then $${}^gb$$ might be used instead of $$g \cdot b$$ in this action.