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.

中文翻译：

---

费米诺维科夫代数承认不变的非退化对称双线性形式

结合流体动力学类型的泊松括号和形式变分微积分中的哈密顿算符引入了诺维科夫代数。Fermionic Novikov 代数对应于超变量中的某个哈密顿超算子。在本文中，我们证明了配备不变非简并对称双线性形式的费米诺维科夫代数是诺维科夫代数。