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Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms. (English) Zbl 07285972

Summary: 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.

MSC:

17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17A30 Nonassociative algebras satisfying other identities
17D25 Lie-admissible algebras
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