Classification of five-dimensional nilpotent Jordan algebras

The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field F of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic ≠2,3. In addition to these algebras we obtained two non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras over an algebraically closed field of characteristic 3.