Logic & Set Theory seminar: Interpretation functors, representation type and decidability
Lorna Gregory, University of Manchester
Howard House 4th floor seminar room
In this talk I will give an overview of recent developments in the model theory of representations of finite-dimensional algebras.
These results will connect representation type with decidability of theories of modules and interpretation functors, an additive version of the model theoretic notion of interpretation.
The representation type of a finite-dimensional k-algebra is a measure of how hard it is to classify its finite-dimensional indecomposable modules. Roughly, a finite-dimensional k-algebra is of wild representation type if classifying its finite-dimensional indecomposable modules is as hard as classifying those of the polynomial ring in two non-commuting variables. On the other hand, a finite-dimensional algebra is tame if for every dimension d, all but finitely many of the finite-dimensional indecomposable modules of dimension d are in finitely many 1-parameter families. According to Drozd, when k is algebraically closed, a finite-dimensional k-algebra is either tame or wild.