TL;DR
This paper introduces BiHom-Akivis algebras, explores their construction from Akivis algebras via twisting, and connects them to other algebraic structures like BiHom-Malcev algebras.
Contribution
It defines BiHom-Akivis algebras and demonstrates their derivation from Akivis algebras through twisting, expanding the understanding of algebraic structures in the BiHom context.
Findings
BiHom-Akivis algebras are introduced and characterized.
The BiHom-commutator-BiHom-associator algebra forms a BiHom-Akivis algebra.
BiHom-Akivis algebras relate to BiHom-Malcev algebras via regular BiHom-alternative algebras.
Abstract
BiHom-Akivis algebras are introduced. The BiHom-commutator-BiHom-associator algebra of a regular BiHom-algebra is a BiHom-Akivis algebra. It is shown that BiHom-Akivis algebras can be obtained from Akivis algebras by twisting along two algebra endomorphisms. It is pointed out that a BiHom-Akivis algebra associated to a regular BiHom-alternative algebra is a BiHom-Malcev algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Sphingolipid Metabolism and Signaling