Novikov superalgebras in low dimensions

TL;DR

This paper classifies low-dimensional Novikov superalgebras, showing that all up to dimension 3 are of type N, which advances understanding of their structure and relation to integrable systems.

Contribution

It introduces a classification dividing Novikov superalgebras into two types and characterizes all low-dimensional cases as type N.

Findings

All Novikov superalgebras of dimension up to 3 are of type N.

Provides a structural classification for low-dimensional Novikov superalgebras.

Abstract

Novikov superalgebras are related to the quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play fundamental role in the completely integrable systems. In this note, we divide Novikov superalgebras into two types: N and S. Then we show that the Novikov superalgebras of dimension up to 3 are of type N.