Classification of orbit closures in the variety of 3-dimensional Novikov algebras

TL;DR

This paper classifies the orbit closures in the variety of 3-dimensional Novikov algebras, providing a detailed hierarchy and invariants to determine degenerations, advancing understanding of their algebraic structure.

Contribution

It introduces a complete classification of orbit closures in 3D Novikov algebras and presents easy-to-compute invariants for degeneration analysis.

Findings

Hasse diagrams of orbit closures are constructed.

Invariants for degeneration are identified and validated.

A comprehensive classification of 3D Novikov algebras is achieved.

Abstract

We classify the orbit closures in the variety Nov_3 of complex, 3-dimensional Novikov algebras and obtain the Hasse diagrams for the closure ordering of the orbits. We provide invariants which are easy to compute and which enable us to decide whether or not one Novikov algebra degenerates to another Novikov algebra.