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<p>Each simple right-alternative singular superalgebrais an extended double.The minimal dimension of an extended doublethat is not a linear superalgebra is&#xa0;10.We consider the 10-dimensional extended doubles of diagonal type and provethat such over an algebraically closed field of characteristic not&#xa0;<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1521_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$ 2 $</EquationSource> </InlineEquation> and&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1521_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$ 3 $</EquationSource> </InlineEquation>has the structure of a superalgebra depending on two parameters.If the ground field is the field of complexesthen we show that the family of simple superalgebrasfor positive real values of the parameters lacks isomorphic superalgebras.</p>

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On Classification of the Right-Alternative Singular 10-Dimensional Superalgebras of Diagonal Type

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • S. V. Pchelintsev

摘要

Each simple right-alternative singular superalgebrais an extended double.The minimal dimension of an extended doublethat is not a linear superalgebra is 10.We consider the 10-dimensional extended doubles of diagonal type and provethat such over an algebraically closed field of characteristic not  $ 2 $ and  $ 3 $ has the structure of a superalgebra depending on two parameters.If the ground field is the field of complexesthen we show that the family of simple superalgebrasfor positive real values of the parameters lacks isomorphic superalgebras.