Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms are Novikov algebras

TL;DR

This paper proves that fermionic Novikov algebras with an invariant non-degenerate symmetric bilinear form are actually Novikov algebras, establishing a key structural property.

Contribution

It demonstrates that such fermionic Novikov algebras necessarily satisfy the Novikov algebra axioms, revealing a fundamental link between these algebraic structures.

Findings

Fermionic Novikov algebras with invariant forms are Novikov algebras

Invariant non-degenerate symmetric bilinear forms impose strong structural constraints

The result simplifies classification of these algebraic structures

Abstract

This paper is to prove that a fermionic Novikov algebra equipped with an invariant non-degenerate symmetric bilinear form is a Novikov algebra.