Central Extensions and Hom-Quadratic Hom-Novikov Color Algebras

Abstract

AbstractThe aim of this paper is to introduce Hom-Novikov color algebra and give some constructions of Hom-Novikov color algebras from a given one and a (weak) morphism. Other constructions using linear operators (bijective linear maps, averaging operators, Rota-Baxter operators, Nijenhuis operators, elements of centroid, derivations), direct sums, multipliers and tensor products are given. We also proved that any Hom-Novikov color algebra is Hom-Lie admissible. Moreover, we introduce Hom-quadratic Hom-Novikov color algebras and provide some properties by twisting. It is also shown that the Hom-Lie color algebra associated to a given quadratic Hom-Novikov color algebra is also quadratic. Finally, we study central extensions of Hom-Novikov color algebras.KeywordsHom-Novikov color algebraLinear operatorsTwistingHom-quadratic Hom-Novikov color algebrasCentral extensions