On classification of the right-alternative singular 10-dimensional superalgebras of diagonal type

Each simple right-alternative singular superalgebra is an extended double. The minimal dimension of an extended double that is not a linear superalgebra is 10. We consider the 10-dimensional extended doubles of diagonal type and prove that such over an algebraically closed field of characteristic not 2 and 3 has the structure of a superalgebra depending on two parameters. If the ground field is the field of complexes then we show that the family of simple superalgebras for positive real values of the parameters lacks isomorphic superalgebras.