The algebraic and geometric classification of $\hat{I}´$-Novikov algebras

Abstract

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

arXiv 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