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<p>A Lie superalgebra is attached to any finite-dimensional <i>J</i>-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from <i>J</i>-ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras.</p>

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J-ternary algebras, structurable algebras, and Lie superalgebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月2日

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  • Isabel Cunha,
  • Alberto Elduque

摘要

A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras, specific of this characteristic, are obtained in this way from J-ternary algebras coming from structurable algebras and, in particular, a new magic square of Lie superalgebras is constructed, with entries depending on a pair of composition algebras.