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Some Results on Novikov–Poisson Algebras

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Abstract

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. A Novikov–Poisson algebra is a Novikov algebra with a compatible commutative associative algebraic structure, which was introduced to construct the tensor product of two Novikov algebras. In this paper, we commence a study of finite-dimensional Novikov–Poisson algebras. We show the commutative associative operation in a Novikov–Poisson algebra is a compatible global deformation of the associated Novikov algebra. We also discuss how to classify Novikov–Poisson algebras. And as an example, we give the classification of 2-dimensional Novikov–Poisson algebras.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Beijing, 100081, People' Republic of China

    Yufeng Zhao

  2. Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, 300071, People' Republic of China

    Chengming Bai

  3. Liu Hui Center for Applied Mathematics, Tianjin, People' Republic of China

    Chengming Bai

  4. Department of Mathematics, Nankai University, Tianjin, People' Republic of China

    Daoji Meng

Authors
  1. Yufeng Zhao
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  2. Chengming Bai
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  3. Daoji Meng
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Correspondence to Yufeng Zhao.

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Zhao, Y., Bai, C. & Meng, D. Some Results on Novikov–Poisson Algebras. International Journal of Theoretical Physics 43, 519–528 (2004). https://doi.org/10.1023/B:IJTP.0000028883.87463.87

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  • DOI: https://doi.org/10.1023/B:IJTP.0000028883.87463.87

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