<p>In this article, we discuss the category <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_496_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal{S}\mathcal{N}_2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">S</mi> <msub> <mi mathvariant="script">N</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_496_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {SSKE}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">SSKE</mi> </math></EquationSource> </InlineEquation> where the objects are skew-supersymmetric bilinear maps. We establish a relation between <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_496_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal{S}\mathcal{N}_2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">S</mi> <msub> <mi mathvariant="script">N</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_496_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {SSKE}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">SSKE</mi> </math></EquationSource> </InlineEquation>. As a result, we discuss the capability of nilpotent Lie superalgebras of class two.</p>

Finite-dimensional nilpotent Lie superalgebras of class two and skew-supersymmetric bilinear maps

期刊论文
发表日期：

2025年2月4日

查看全文

Ibrahem Yakzan Hasan,
Rudra Narayan Padhan

摘要

In this article, we discuss the category $\mathcal{S}\mathcal{N}_2$ $S N_{2}$ where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category $\mathcal {SSKE}$ $SSKE$ where the objects are skew-supersymmetric bilinear maps. We establish a relation between $\mathcal{S}\mathcal{N}_2$ $S N_{2}$ and $\mathcal {SSKE}$ $SSKE$ . As a result, we discuss the capability of nilpotent Lie superalgebras of class two.