2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146085We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the spirit of approach of the papers \cite{VO,OV} to representation theory of symmetric groups. The main example is the classical - theory of the projective representations of symmetric groups.30 pp. Ref.23Representation TheoryQuantum Algebra20C30text