Classification of three-dimensional Jordan superalgebras

Abstract

In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer to the problem of determining the minimal dimension of exceptional Jordan superalgebras. Our strategy to provide a lower bounded for this dimension is to determine the complete list of Jordan superalgebras of small dimensions and verify which ones are special or exceptional.