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<p>Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative non-associative algebras. In previous work, we gave an explicit description of these algebras for groups of type <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="31_2025_9923_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\( G_2,F_4 \)</EquationSource> </InlineEquation> and certain forms of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="31_2025_9923_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\( E_6 \)</EquationSource> </InlineEquation> in terms of octonion and Albert algebras. In this paper, we extend this further by dealing with <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="31_2025_9923_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\( E_7 \)</EquationSource> </InlineEquation> in terms of generalised Freudenthal triple systems.</p>

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Non-associative Frobenius Algebras of Type \( E_7 \)

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • Jari Desmet

摘要

Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative non-associative algebras. In previous work, we gave an explicit description of these algebras for groups of type \( G_2,F_4 \) and certain forms of \( E_6 \) in terms of octonion and Albert algebras. In this paper, we extend this further by dealing with \( E_7 \) in terms of generalised Freudenthal triple systems.