Gnatyuk E. Differential graded categories and quadratic forms

The thesis is devoted to the investigation of differential graded categories, namely, to the classification theorems for differential graded categories with positive definite quadratic form and with semi-definite quadratic form as to their representation type. The first basic idea is an assertion that the representation type of differential graded category with underlying bigraph of a Dynkin and affine type is well described. The second idea is to use some kind of reductions of differential graded category together with its quadratic form that preserve the representation type in order to simplify the problem. Dynkin oriented graphs, non oriented graphs, partly oriented graphs and graphs with multiple edges arise in various fields of mathematics such as group theory, theory of quivers, theory of simple Lie algebras and others. They are used for classification of different mathematical objects.