On derivations of Leibniz algebras

Kailash C. Misra; Sutida Patlertsin; Suchada Pongprasert; Thitarie Rungratgasame; Kailash C. Misra; Sutida Patlertsin; Suchada Pongprasert; Thitarie Rungratgasame

doi:10.3934/era.2024214

Electronic Research Archive

2024, Volume 32, Issue 7: 4715-4722. doi: 10.3934/era.2024214

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Research article

On derivations of Leibniz algebras

1.
Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
2.
Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok, Thailand

Received: 12 May 2024 Revised: 10 July 2024 Accepted: 17 July 2024 Published: 29 July 2024

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras.
- Leibniz algebra,
- completeness,
- extension,
- holomorph,
- derivation,
- direct sum,
- decomposition
Citation: Kailash C. Misra, Sutida Patlertsin, Suchada Pongprasert, Thitarie Rungratgasame. On derivations of Leibniz algebras[J]. Electronic Research Archive, 2024, 32(7): 4715-4722. doi: 10.3934/era.2024214

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Abstract

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras.

References

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