The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation

Muhammad Arief Budiman, Edi Kurniadi, Sukono Sukono

Abstract


The structure of a g-quasi-Frobenius Lie Algebra can be realized as a quasi-Frobenius Lie Algebra modules over a Lie Algebra g. This research discusses a special condition of the g-quasi-Frobenius Lie Algebra, namely when g acts on its self. This condition supports the construction of an inner derivation on g. The criterion investigated is the characterization of the g-quasi-Frobenius Lie Algebra in relation to the inner derivation. The result obtained is a criterion: a g-quasi-Frobenius Lie Algebra can be constructed on g itself if and only if the inner derivation is zero. Furthermore, several concrete examples are provided to test this criterion.

Keywords


Frobenius Lie Algebra; quasi-Frobenius Lie Algebra; Inner Derivation; Lie Algebra Structure; g-quasi-Frobenius Lie Algebra.

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DOI: https://doi.org/10.18860/cauchy.v11i1.41601

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