Codimension Growth and Non-Koszulity of Novikov Operad

Abstract

An algebra with identities a ○ (b ○ c − c ○ b) = (a ○ b) ○ c − (a ○ c) ○ b and a ○ (b ○ c) = b ○ (a ○ c) is called Novikov. We construct free Novikov base in terms of Young diagrams. We show that codimensions exponent for a variety of Novikov algebras exists and is equal to 4. We prove that Novikov operad is not Koszul.