A new approach to the representation theory of the symmetric groups. IV. $ \Bbb Z_{2}$-graded groups and algebras

A. M. Vershik, A. N. Sergeev

Published 2008-01-16Version 1

We 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.