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<p>The algebraic and geometric classifications of complex 3-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of complex 3-dimensional Kokoris and standard superalgebras, and, due to one-to-one correspondences between suitable superalgebras, we have classifications for generic Poisson–Jordan and generic Poisson superalgebras. As a byproduct, we have the algebraic and geometric classification of the variety of complex 3-dimensional anticommutative superalgebras and their principal subvarieties: Lie, Malcev, binary Lie, Tortkara, anticommutative <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak {CD}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">CD</mi> </math></EquationSource> </InlineEquation>-, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {s}_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="fraktur">s</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation>-, anticommutative terminal superalgebras, anticommutative conservative and anticommutative quasi-conservative (rigid) superalgebras; and also prove a Grishkov–Shestakov’s conjecture for 3-dimensional binary Lie superalgebras.</p>

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The Algebraic and Geometric Classification of Noncommutative Jordan Superalgebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月30日

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  • Hani Abdelwahab,
  • Ivan Kaygorodov,
  • Abror Khudoyberdiyev

摘要

The algebraic and geometric classifications of complex 3-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of complex 3-dimensional Kokoris and standard superalgebras, and, due to one-to-one correspondences between suitable superalgebras, we have classifications for generic Poisson–Jordan and generic Poisson superalgebras. As a byproduct, we have the algebraic and geometric classification of the variety of complex 3-dimensional anticommutative superalgebras and their principal subvarieties: Lie, Malcev, binary Lie, Tortkara, anticommutative \(\mathfrak {CD}\) CD -, \(\mathfrak {s}_4\) s 4 -, anticommutative terminal superalgebras, anticommutative conservative and anticommutative quasi-conservative (rigid) superalgebras; and also prove a Grishkov–Shestakov’s conjecture for 3-dimensional binary Lie superalgebras.