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.
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页码：12 / 29
页数：18
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