A Hom-version of the affinizations of Balinskii-Novikov and Novikov superalgebras

In this paper, we introduce the notions of Hom-Balinskii-Novikov and Hom-Novikov superalgebras, in which the defining identities are twisted by homomorphisms. Then we construct some infinite-dimensional Hom-Lie superalgebras by the affinizations of the above two Hom-superalgebras. Moreover, we apply the bilinear forms with some invariance conditions on the Hom-Balinskii-Novikov and Hom-Novikov superalgebras to construct central extensions of the infinite-dimensional Hom-Lie superalgebras. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3546025]