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Supercommutator (Hom-)superalgebras of right (Hom-)alternative superalgebras

Volume 164 / 2021

A. Nourou Issa Colloquium Mathematicum 164 (2021), 11-42 MSC: Primary 17D99; Secondary 17A30, 17A70, 17B61, 17D15. DOI: 10.4064/cm7984-12-2019 Published online: 7 August 2020


It is shown that the supercommutator superalgebra of a right alternative superalgebra is a Bol superalgebra. Hom-Bol superalgebras are defined and it is shown that they are closed under even self-morphisms. Any Bol superalgebra along with any even self-morphism is twisted into a Hom-Bol superalgebra. The supercommutator superalgebra of a right Hom-alternative superalgebra has a natural Hom-Bol structure. In order to prove this last result, the Hom-Jordan-admissibility of right Hom-alternative superalgebras is investigated and next Hom-Jordan supertriple systems are defined and their connection with Hom-Jordan superalgebras and Hom-Lie supertriple systems is considered.


  • A. Nourou IssaDépartement de Mathématiques
    Université d’Abomey-Calavi
    01 BP 4521 Cotonou 01, Benin

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