Novikov algebras and Novikov structures on Lie algebras

被引：15

作者：

Burde, Dietrich ^{[2
]}

Dekimpe, Karel ^{[1
]}

Vercammen, Kim ^{[1
]}

机构：

[1] Katholieke Univ Leuven, B-8500 Kortrijk, Belgium

[2] Univ Vienna, Fak Math, A-1090 Vienna, Austria

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2008年 / 429卷 / 01期

关键词：

Novikov algebra; Novikov structure; filiform Lie algebra; nilpotent Lie algebra; solvable Lie algebra;

D O I：

10.1016/j.laa.2008.01.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any free three-step nilpotent Lie algebra admits a Novikov structure. We study the existence question also for Lie algebras of triangular matrices. Finally we show that there are families of Lie algebras of arbitrary high solvability class which admit Novikov structures. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：31 / 41

页数：11