Commutative post-Lie algebra structures on Lie algebras

被引：30
|
作者：
Burde, Dietrich [1 ]
Moens, Wolfgang Alexander [1 ]
机构：
[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
JOURNAL OF ALGEBRA | 2016年 / 467卷
基金：
奥地利科学基金会;
关键词：
Post-Lie algebra; Pre-Lie algebra; GENERALIZED DERIVATIONS; AFFINE STRUCTURES;
D O I：
10.1016/j.jalgebra.2016.07.030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that any CPA-structure (commutative post-Lie algebra structure) on a perfect Lie algebra is trivial. Furthermore we give a general decomposition of inner CPA-structures, and claAsify all CPA-structures on complete Lie algebras. As a special case we obtain the CPA-structures of parabolic subalgebras of semisimple Lie algebras. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：183 / 201
页数：19
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