On the finite dimensional representations of the pseudo-Lie algebras (Q1238880)

In the note the author obtains a structure of the pseudo-Lie algebra (graded Lie algebra) of generators of supersymmetry assuming that it has a faithful, finite dimensional representation [at present the question whether Ado's theorem is true for pseudo-Lie algebras is affirmatively answered in the paper by \textit{V. G. Kac} [Commun. Math. Phys. 53, 31--64 (1977; Zbl 0359.17009)] in a space of minimal possible dimension at which there is still a faithful representation of the Poincaré Lie algebra.