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

A. Nourou Issa
2020 Colloquium Mathematicum  
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
more » ... t 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.
doi:10.4064/cm7984-12-2019 fatcat:kwccsexwdzajrmpv5ip3hb4bqe