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On Inner Derivations of Leibniz Algebras

Author

Listed:
  • Sutida Patlertsin

    (Department of Mathematics, Faculty of Science, Srinakharinwirot University, 114 Sukhumvit 23, Bangkok 10110, Thailand)

  • Suchada Pongprasert

    (Department of Mathematics, Faculty of Science, Srinakharinwirot University, 114 Sukhumvit 23, Bangkok 10110, Thailand)

  • Thitarie Rungratgasame

    (Department of Mathematics, Faculty of Science, Srinakharinwirot University, 114 Sukhumvit 23, Bangkok 10110, Thailand)

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.

Suggested Citation

  • Sutida Patlertsin & Suchada Pongprasert & Thitarie Rungratgasame, 2024. "On Inner Derivations of Leibniz Algebras," Mathematics, MDPI, vol. 12(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1152-:d:1374125
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