William Crawley-Boevey: String algebras, Dedekind-like rings and clannish algebras, revisited

String algebras (or a slight variation, special biserial algebras) are a class of associative algebras whose indecomposable modules can be described as certain "string" or "band" modules, using the methods of Gelfand and Ponomarev. Dedekind-like rings are a related class of commutative noetherian rings, whose finitely generated modules have been classified by Klingler and Levy (apart from an exceptional case). Clannish algebras are a generalization of string algebras introduced by the speaker in the 1980s. In this talk I shall review the theory of clannish algebras, discuss a version which involves field extensions, and outline a possible approach to Klingler and Levy’s exceptional rings.