Supercommutator algebras of right (Hom-)alternative superalgebras

Abstract

The supercommutator algebra 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 algebra of a right Hom-alternative superalgebra has a natural Hom-Bol superalgebra structure.

References in corpus (3)

• Hom-algebras and homology
• Right Hom-alternative algebras
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras