The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence

摘要

Let P-n = Kx(1),..., x(n) be a polynomial algebra over a field K of characteristic zero and Dip(n)(0) (respectively, dip(n)(c)) be the Lie algebra of derivations of P-n with zero (respectively, constant) divergence. We prove that Aut(Lie)(dip(n)(0)) similar or equal to Aut(K-alg)(P-n) (n >= 2) and Aut(Lie)(dip(n)(c)) similar or equal to Aut(K-alg)(P-n). The Lie algebra dip(n)(c) is a maximal Lie subalgebra of Der(K)(P-n) Minimal finite sets of generators are found for the Lie algebras dip(n)(0) and dipp(n)(c).