Derivations of two-step nilpotent algebras

被引：3
作者：
La Rosa, Gianmarco [1 ]
Mancini, Manuel [1 ,2 ]
机构：
[1] Univ Palermo, Dipartimento Matemat & Informat, Palermo, Italy
[2] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy
来源：
COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 12期
关键词：
Almost inner derivation; derivation; Lie algebra; Lie theory; Leibniz algebra; nilpotent Leibniz algebra; INNER DERIVATIONS; LIE-ALGEBRAS;
D O I：
10.1080/00927872.2023.2222415
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every almost inner derivation of a complex nilpotent Leibniz algebra with one-dimensional commutator ideal, with three exceptions, is an inner derivation.
引用
收藏
页码：4928 / 4948
页数：21
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