The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence. Issue 3 (4th March 2017) - Bavula, V. V.
ABSTRACT: Let P n  =  K [ x 1, …, x n ] be a polynomial algebra over a field K of characteristic zero and𝔡 𝔦 𝔳 n 0 (respectively, 𝔡 𝔦 𝔳 n c ) be the Lie algebra of derivations of P n with zero (respectively, constant) divergence. We prove thatAut Lie ( 𝔡 𝔦 𝔳 n 0 ) ≈ Aut K − alg ( P n ) ( n  ≥ 2) andAut Lie ( 𝔡 𝔦 𝔳 n c ) ≈ Aut K − alg ( P n ) . The Lie algebra𝔡 𝔦 𝔳 n c is a maximal Lie subalgebra of Der K ( P n ). Minimal finite sets of generators are found for the Lie algebras𝔡 𝔦 𝔳 n 0 and𝔡 𝔦 𝔳 n c .