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Abstract <p> We consider holomorphic realizations in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1174_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb C^4\)</EquationSource> </InlineEquation> for a large family of 7-dimensional Lie algebras containing a 6-dimensional nilradical and one or two 4-dimensional abelian subalgebras. We show that for these Lie algebras, a natural condition of having tubular Levi-nondegenerate 7-dimensional orbits is rarely compatible with a straightened basis of one of the abelian subalgebras. In many cases, this incompatibility follows easily from the structure and properties of abelian ideals in 4-dimensional subalgebras of the algebras in question. </p>

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On the Amount of Nondegenerate Tubular Orbits of 7-Dimensional Lie Algebras in \(\mathbb C^4\)

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Valeria Kaverina,
  • Alexander Loboda

摘要

Abstract

We consider holomorphic realizations in \(\mathbb C^4\) for a large family of 7-dimensional Lie algebras containing a 6-dimensional nilradical and one or two 4-dimensional abelian subalgebras. We show that for these Lie algebras, a natural condition of having tubular Levi-nondegenerate 7-dimensional orbits is rarely compatible with a straightened basis of one of the abelian subalgebras. In many cases, this incompatibility follows easily from the structure and properties of abelian ideals in 4-dimensional subalgebras of the algebras in question.