Extensions of pseudo-euclidean mock-Lie superalgebras

In this article, we introduce mock-Lie superalgebras, we give some definitions, properties, constructions, and we study their representations. Moreover we introduce pseudo-euclidean mock-Lie superalgebras which are mock-Lie superalgebras with even non-degenerate supersymmetric and invariant bilinear forms. Finally, we study the double extensions and generalized double extensions of mock-Lie superalgebras and their isometries.