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

被引：1

作者：

Bavula, V. V. ^{[1
]}

机构：

[1] Univ Sheffield, Dept Pure Math, Hicks Bldg, Sheffield S3 7RH, S Yorkshire, England

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Automorphism; derivation; group of automorphisms; Lie algebra; locally nilpotent derivation; the divergence; the Lie algebras of polynomial vector fields with zero or constant divergence;

D O I：

10.1080/00927872.2016.1175596

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P-n = K[x(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).

引用

页码：1114 / 1133

页数：20

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