Suppose I have a Hamiltonian $H$ with first integrals $L_1, \ldots, L_k$ on a symplectic manifold $M$ such that $\{H,L_i\}=0$, and suppose that there are constants $c_{pq}^r$ such that $\{L_p,L_q\}=\sum_r c_{pq}^r L_r$. In this case $c_{pq}^r$ are structure constants of a Lie algebra $\mathfrak{g}$ (the Lie algebra spanned by $L_i$'s).
I have trouble in how to the construct the momentum map $\mu: M \rightarrow \mathfrak{g}$ in this general setting. Is $\mu$ just given by $(L_1,L_2, \ldots , L_k)$? Could somebody explain this to me?