The map $\mu:M\rightarrow{\scriptstyle{\cal G}}^{*}$ is called a moment map if it satisfies the following property:

$$\omega(\cdot,v)=\mu^{*}(da).$$

(24)

Here $da$ is the natural linear $1$ -form on ${\scriptstyle{\cal G}}^{*}$ taking values in ${\scriptstyle{\cal G}}^{*}$ .