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<p>We study the conditions under which the well-known forgetful and so-called Daletskii–Takhtajan’s functors between the categories of Leibniz and Leibniz <i>n</i>-algebras preserve central derivations and centroids. On the other hand, we introduce and study skew-symmetric bi-derivations and commuting linear maps of Leibniz algebras, and under appropriate conditions, we relate them to centroids.</p>

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Central Derivations, Centroids and Skew-Symmetric Bi-derivations of Leibniz (n-)Algebras

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  • 发表日期：

    2025年5月20日

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  • José Manuel Casas,
  • Emzar Khmaladze,
  • Manuel Ladra

摘要

We study the conditions under which the well-known forgetful and so-called Daletskii–Takhtajan’s functors between the categories of Leibniz and Leibniz n-algebras preserve central derivations and centroids. On the other hand, we introduce and study skew-symmetric bi-derivations and commuting linear maps of Leibniz algebras, and under appropriate conditions, we relate them to centroids.