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arXiv · 2008.04026

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

A. Nourou Issa
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Abstract

It 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.

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A. Nourou Issa. 2020-08-10. Supercommutator (Hom-)superalgebras of right (Hom-)alternative superalgebras. https://arxiv.org/abs/2008.04026

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