The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Bavula, V. V.
• Is Part Of: Communications in algebra. Volume 45:Issue 3(2017)
• Page Start: 1114
• Page End: 1133
• Publication Date: 2017-03-04
• Subjects: Automorphism -- derivation -- group of automorphisms -- Lie algebra -- locally nilpotent derivation -- the divergence -- the Lie algebras of polynomial vector fields with zero or constant divergence; 17B40 -- 17B20 -- 17B66 -- 17B65 -- 17B30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1175596
• Languages: English
• ISSNs: 0092-7872

Abstract

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 .