ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON SPACES OF JACOBI DIAGRAMS. II

Abstract The automorphism group $\operatorname {Aut}(F_n)$ of the free $F_n$ acts on a space $A_d(n)$ Jacobi diagrams degree d n oriented arcs. We study -module structure by using two actions associated graded vector : an action general linear {GL}(n,\mathbb {Z})$ and Lie algebra $\mathrm {gr}(\operatorname {IA}(n))$ IA-automorphism {IA}(n)$ with its lower central series. extend to Andreadakis filtration endomorphism monoid . By this action, we obtain indecomposable decomposition as -modules for $n\geq 2d$ Moreover, radical socle $A_3(n)$