Supercommutator (Hom-)superalgebras of right (Hom-)alternative superalgebras
Volume 164 / 2021
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
Abstract
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.
