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# A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations

Abstract and Applied Analysis (Impact Factor: 1.1). 01/2013; 2013. DOI: 10.1016/S0550-3213(01)00405-9

Source: arXiv

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**ABSTRACT:**Novikov superalgebras are related to the quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play fundamental role in the completely integrable systems. In this note, we divide Novikov superalgebras into two types: N and S. Then we show that the Novikov superalgebras of dimension up to 3 are of type N.04/2009; - [Show abstract] [Hide abstract]

**ABSTRACT:**We give a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic. Moreover, we introduce “Novikov–Poisson algebras” and their tensor theory. Our tensor theory enables us to understand better certain finite-dimensional simple Novikov algebras and their irreducible modules.Journal of Algebra - J ALGEBRA. 01/1996; 185(3):905-934. - [Show abstract] [Hide abstract]

**ABSTRACT:**We prove that an algebraic structure proposed by Gel''fand and Dorfman in studying Hamiltonian operators is equivalent to an associative algebra with a derivation under a unitary condition.Letters in Mathematical Physics 12/1994; 33(1):1-6. · 2.42 Impact Factor

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