Hom-Novikov algebras

Details Hom-Novikov algebras Hom-Novikov algebras

2009-09-03

arxiv.org/abs/0909.0726v2

Journal of Physics A 44 (2011) 085202

Mathematics

Rings and Algebras

To appear in Journal of Physics A

Scientific paper

10.1088/1751-8113/44/8/085202

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.

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