Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 953-958, 2020
Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms
Zhiqi Chen, Xueqing Chen, Ming Ding
Received February 21, 2019. Published online March 31, 2020.
Abstract: Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras.
Keywords: Novikov algebra; fermionic Novikov algebra; invariant bilinear form
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Affiliations: Zhiqi Chen, School of Mathematical Sciences and LPMC, Nankai University, Tianjin, P. R. China, e-mail: chenzhiqi@nankai.edu.cn; Xueqing Chen, Department of Mathematics, University of Wisconsin-Whitewater, 800 W. Main Street, Whitewater, WI 53190, USA, e-mail: chenx@uww.edu; Ming Ding (corresponding author), School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, P. R. China, e-mail: m-ding04@mails.tsinghua.edu.cn
