The algebraic and geometric classification of $\delta$-Novikov algebras

Abstract

The notion of $\delta$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $\delta$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have a $2$-dimensional simple algebra for $\delta =-1.$ The present paper is dedicated to the study of $3$-dimensional $\delta$-Novikov algebras for $\delta \notin \{0,1\}.$ The algebraic and geometric classifications of complex $3$-dimensional $\delta$-Novikov algebras are given. As a corollary, we prove that there are no simple $3$-dimensional $\delta$-Novikov algebras.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2505.00720, arXiv:2601.22110, arXiv:2407.05429, arXiv:2408.07078, arXiv:2307.00289, arXiv:2308.00374, arXiv:2205.00444

References in corpus (8)

• The algebraic and geometric classification of nilpotent Novikov algebras
• Novikov structures on solvable Lie algebras
• Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
• A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
• Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras
• Polynomial identities in Novikov algebras
• Noncommutative Novikov algebras
• Semiprime Novikov Algebras

Cited by in corpus (1)

• The algebraic and geometric classification of derived Jordan and bicommutative algebras