Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras

被引：9

作者：

Burde, Dietrich ^{[1
]}

Dekimpe, Karel ^{[2
]}

Moens, Wolfgang Alexander ^{[1
]}

机构：

[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Katholieke Univ Leuven Kulak, E Sabbelaan 53 Bus 7657, B-8500 Kortrijk, Belgium

来源：

JOURNAL OF ALGEBRA | 2019年 / 526卷

基金：

奥地利科学基金会;

关键词：

Post-Lie algebra; Pre-Lie algebra; CPA structure; Free-nilpotent Lie algebra; AFFINE STRUCTURES;

D O I：

10.1016/j.jalgebra.2019.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for a given nilpotent Lie algebra g with Z(g) subset of [g, g] all commutative post-Lie algebra structures, or CPA-structures, on g are complete. This means that all left and all right multiplication operators in the algebra are nilpotent. Then we study CPA-structures on free-nilpotent Lie algebras F-g,F-c and discover a strong relationship to solving systems of linear equations of type [x, u] + [y, v] = 0 for generator pairs x, y is an element of F-g,F-c. We use results of Remeslennikov and Stohr concerning these equations to prove that, for certain g and c, the free-nilpotent Lie algebra F-g,F-c has only central CPA-structures. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：12 / 29

页数：18

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