A new approach to the representation theory of the symmetric groups. IV. Z₂-graded groups and algebras

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We start with definitions of the general notions of the theory of Z₂-graded algebras. Then we consider theory of inductive families of Z₂-graded semisimple finite-dimensional algebras and its representations in the spirit of approach of the papers VO,OV to representation theory of symmetric groups. The main example is the classical - theory of the projective representations of symmetric groups.