Generalized Jacobi identities and Jacobi elements of the group ring of the symmetric group

Sergei O. Ivanov, Savelii Novikov

By definition the identities $[x_1,x_2]+[x_2,x_1]=0$ and $[x_1,x_2,x_3]+[x_2,x_3,x_1]+[x_3,x_1,x_2]=0$ hold in any Lie algebra. It is easy to check that the ident…