Zembyk V. Representations of nodal finite dimensional algebras

The thesis is devoted to the study of the structure of nodal algebras and their representations. The structure of nodal algebras over an arbitrary field is described. Furthermore, a specialisation of these results over an algebraically closed field is investigated. It is shown that nodal algebras are obtained from hereditary algebras using some operations on these simple components. It is proved that all gentle and skewed-gentle algebras are nodal and conditions are given for a nodal algebra to be gentle or skewed-gentle. Then the nodal algebras related to the hereditary algebras of Dynkin types and of Euclidean types are investigated and their representation types (finite, or tame, or wild) are established.