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Transitive Novikov Algebras on Four-Dimensional Nilpotent Lie 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. The commutator of a Novikov algebra is a Lie algebra, and the radical of a finite-dimensional Novikov algebra is transitive. In this paper, we give a classification of transitive Novikov algebras on four-dimensional nilpotent Lie algebras based on Kim (1986, Journal of Differential Geometry 24, 373–394).

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Authors and Affiliations

  1. Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, People's Republic of China

    Chengming Bai

  2. The Key Laboratory of Pure Mathematics and Combinatorics, Ministry of Education, People's Republic of China

    Chengming Bai & Daoji Meng

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

    Daoji Meng

Authors
  1. Chengming Bai
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  2. Daoji Meng
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Bai, C., Meng, D. Transitive Novikov Algebras on Four-Dimensional Nilpotent Lie Algebras. International Journal of Theoretical Physics 40, 1761–1768 (2001). https://doi.org/10.1023/A:1011968631980

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