Kyrychenko A. *-Algbras generated by linear connected projections, their representations and applications

The thesis is devoted to the investigations of algebras with an involution by operators in Hilbert space. The structure of finite dimension algebras generated by linear connected idempotents is described. The description of the set of the coefficients to which algebras generated by four linear connected idempotents has nonzero representations and *-representations of such algebras are described by functors of Coxeter. The problem of description of operators with two point spectrum which are a sum of three projections is solved. Some two-parameters sets of coefficients to which exists linear combination of projections equal to the identity are considered. New $*$-wild algebras generated by linear connected projections are described