The groups of automorphisms of the Lie algebras of triangular polynomial derivations

The group of automorphisms Gn of the Lie algebra un of triangular polynomial derivations of the polynomial algebra Pn=K[x1,…,xn] is found (n⩾2), it is isomorphic to an iterated semi-direct productTn⋉(UAutK(Pn)n⋊(Fn′×En)) where Tn is an algebraic n-dimensional torus, UAutK(Pn)n is an explicit factor group of the group UAutK(Pn) of triangular polynomial automorphisms, Fn′ and En are explicit groups that are isomorphic respectively to the groups I and Jn−2 where I:=(1+t2K〚t〛,⋅)≃KN and J:=(tK〚t〛,+)≃KN. It is shown that the adjoint group of automorphisms of the Lie algebra un is equal to the group UAutK(Pn)n.