Publication: On Inner Derivations of Leibniz Algebras
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Issued Date
2024-04-01
Resource Type
eISSN
22277390
Scopus ID
2-s2.0-85191370006
Journal Title
Mathematics
Volume
12
Issue
8
Rights Holder(s)
SCOPUS
Bibliographic Citation
Mathematics Vol.12 No.8 (2024)
Suggested Citation
Patlertsin S., Pongprasert S., Rungratgasame T. On Inner Derivations of Leibniz Algebras. Mathematics Vol.12 No.8 (2024). doi:10.3390/math12081152 Retrieved from: https://hdl.handle.net/20.500.14740/20265
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Abstract
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.