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<p>The five-dimensional anti-commutative algebras having an analogous family of flags of subalgebras as the solvable Malcev algebras form the class of Malcev-like algebras. Recently a classification of the binary Lie algebras in this class is achieved. Our investigation extends this result. We determine Malcev-like algebras over a field <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2367_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {K}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">K</mi> </math></EquationSource> </InlineEquation> of characteristic zero. These algebras are extensions of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2367_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {K}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">K</mi> </math></EquationSource> </InlineEquation> by a 4-dimensional nilpotent Lie algebra and simultaneously semidirect sums of the two-dimensional non-abelian Lie algebra and an abelian algebra. We find normal forms of their multiplications and describe their isomorphism classes.</p>

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5-Dimensional Malcev-Like Algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月18日

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  • Kornélia Ficzere,
  • Ágota Figula

摘要

The five-dimensional anti-commutative algebras having an analogous family of flags of subalgebras as the solvable Malcev algebras form the class of Malcev-like algebras. Recently a classification of the binary Lie algebras in this class is achieved. Our investigation extends this result. We determine Malcev-like algebras over a field \({\mathbb {K}}\) K of characteristic zero. These algebras are extensions of \({\mathbb {K}}\) K by a 4-dimensional nilpotent Lie algebra and simultaneously semidirect sums of the two-dimensional non-abelian Lie algebra and an abelian algebra. We find normal forms of their multiplications and describe their isomorphism classes.