Extensions of pseudo-euclidean mock-Lie superalgebras

In this paper, we introduce mock-Lie superalgebras, give some definitions, properties, constructions, and 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.