Hom-Novikov algebras

Abstract

We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions two or three are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

To appear in Journal of Physics A

References in corpus (2)

• A Unified Algebraic Approach to Classical Yang-Baxter Equation
• Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras

Cited by in corpus (8)

• Hom-Lie 2-algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• The construction and deformation of BiHom-Novikov agebras
• Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras
• On split regular Hom-Lie superalgebras
• Another approach to Hom-Lie bialgebras via Manin triples
• Tensor products and perturbations of BiHom-Novikov-Poisson algebras
• Deforming algebras with anti-involution via twisted associativity