Classification of Balinsky–Novikov superalgebras with dimension 2|2

Abstract

The notion of Balinsky–Novikov (BN) superalgebra was introduced to construct super-Virasoro-type Lie superalgebras. We classify the 2|2-dimensional complex BN superalgebras whose odd parts’ products are not zero. In addition to the known results on the classification of 2|2-dimensional Novikov superalgebras, we give an explicit comparison among them and their associated Lie superalgebras. As an application, we construct some Lie superalgebras whose even parts are the W(2, 2) Lie algebra. Finally, we reformulate the classification results in terms of the even parts being the known classification results of two-dimensional Novikov algebras.