Systems of $n$ subspaces and representations of $*$-algebras generated   by projections
  In this paper we study a relationship between systems of $n$ subspaces and representations of $*$-algebras generated by projections. We prove that irreducible nonequivalent $*$-representations of $*$-algebras $\mathcal P_{4,com}$ generate all nonisomorphic transitive quadruples of subspaces of a finite dimensional space. 
Yu. P. Moskaleva, Yu. S. Samoilenko