Algebras of Dihedral Type and Universal Deformation Rings

Our goal is to use combinatorial methods to determine universal deformation rings of representations. Quivers, which are directed graphs, provide a combinatorial framework for the study of representations of algebras. Suppose k is an algebraically closed field. We look at a special class of k-algebras, called special biserial algebras, which are defined by certain quivers and relations and for which all representations are given combinatorially using so-called strings and bands. We show how to determine the universal deformation rings for certain representations given by strings.