On the algebraic variety of Hom-Lie algebras

Remm, Elisabeth; Goze, Michel

doi:10.48550/arxiv.1706.02484

Cited by 1 publication

(1 citation statement)

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“…In [72], the special cases of nilpotent and filiform Hom-Lie algebras are studied and classified up to dimension 7. In [73], the algebraic varieties of Hom-Lie algebras over the complex numbers are considered; it is shown that all 3-dimensional skewsymmetric algebras can be Hom-Lie algebras, but this is not true for the 4-dimensional case. Some more properties of the algebraic varieties of Hom-Lie algebras are studied.…”

Section: Introductionmentioning

confidence: 99%

On Properties and Classification of a Class of 4-Dimensional 3-Hom-Lie Algebras with a Nilpotent Twisting Map

Kitouni,

Silvestrov

2024

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The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map α and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-isomorphic subclasses. The levels of solvability and nilpotency of the 3-Hom-Lie algebras in these five classes are obtained. Building upon that, all algebras of this class are classified up to Hom-algebra isomorphism. Necessary and sufficient conditions for multiplicativity of general (n+1)-dimensional n-Hom-Lie algebras, as well as for algebras in the considered class, are obtained in terms of the structure constants and the twisting map. Furthermore, for some algebras in this class, it is determined whether the terms of the derived and central descending series are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals.

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Section: Introductionmentioning

confidence: 99%