Dyachenko S. Pointwise projektive representations of marked quivers

The dissertation is devoted to the study of the one-sided equivalence matrices problem and to the study of the pointwise projective representations of Alg-marked quivers. The main results of the dissertation is the description of all Alg-marked quivers of pointwise projective tame and finite type and the description of all one sided tame and finite basis algebras. It is proved that the underline graph of the Alg-marked quiver of finite type is a Dynkin diagram, and that the underline graph of the Alg-marked quiver of tame type is Dynkin diagram or extended Dynkin diagram. The problem of pointwise projective representations of Alg-marked quiver is reduced to the case of connected quiver marked by indecomposable algebras. It is proved that there exists a multiplicative basis for algebras corresponding to tame marked quivers.