A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations

Abstract and Applied Analysis (Impact Factor: 1.27). 01/2013; 2013. DOI: 10.1155/2013/270937
Source: arXiv


We construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.

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    • "Bai and Meng [2] [3] [4] did a series of researches on low dimensional Novikov algebras, such as the structure and classification. Chen construct two kinds of Novikov algebras [5] [6] . "
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    ABSTRACT: We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and Hom-Novikov superalgebras with Rota-Baxter operators, respectively. We show that quadratic Hom-Novikov superalgebras are Hom-associative superalgebras and the sub-adjacent Hom-Lie superalgebras of Hom-Novikov superalgebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of Hom-Novikov superalgebras.


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