Algebraic Constructions for Novikov–Poisson Algebras

Naping Bao and Yanyong Hong ()
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Naping Bao: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Yanyong Hong: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Mathematics, 2022, vol. 10, issue 17, 1-18

Abstract: A Novikov–Poisson algebra ( A , ∘ , · ) is a vector space with a Novikov algebra structure ( A , ∘ ) and a commutative associative algebra structure ( A , · ) satisfying some compatibility conditions. Give a Novikov–Poisson algebra ( A , ∘ , · ) and a vector space V . A natural problem is how to construct and classify all Novikov–Poisson algebra structures on the vector space E = A ⊕ V such that ( A , ∘ , · ) is a subalgebra of E up to isomorphism whose restriction on A is the identity map. This problem is called extending structures problem. In this paper, we introduce the definition of a unified product for Novikov–Poisson algebras, and then construct an object GH 2 ( V , A ) to answer the extending structures problem. Note that unified product includes many interesting products such as bicrossed product, crossed product and so on. Moreover, the special case when dim ( V ) = 1 is investigated in detail.

Keywords: Novikov–Poisson algebra; Novikov algebra; extending structures; crossed product; bicrossed product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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