On Inner Derivations of Leibniz Algebras

被引:1
|
作者
Patlertsin, Sutida [1 ]
Pongprasert, Suchada [1 ]
Rungratgasame, Thitarie [1 ]
机构
[1] Srinakharinwirot Univ, Fac Sci, Dept Math, 114 Sukhumvit 23, Bangkok 10110, Thailand
关键词
Leibniz algebra; Lie algebra; derivation; inner derivation; central derivation; completeness; semisimple;
D O I
10.3390/math12081152
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras. In this work, we demonstrate that the algebra of inner derivations of a Leibniz algebra can be decomposed into the sum of the algebra of left multiplications and a certain ideal. Furthermore, we show that the quotient of the algebra of derivations of the Leibniz algebra by this ideal yields a complete Lie algebra. Our results independently establish that any derivation of a semisimple Leibniz algebra can be expressed as a combination of three derivations. Additionally, we compare the properties of the algebra of inner derivations of Leibniz algebras with the algebra of central derivations.
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页数:9
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