Jordan recoverability of some categories of modules over gentle algebras

Abstract: Gentle algebras form a class of finite dimensional algebras introduced by Assem and Skowroński in the 80’s. Indecomposable modules over such an algebra admit a combinatorial description in terms of strings and bands, which are walks in the associated gentle quiver (satisfying some further conditions), thanks to the work of Butler and Ringel. A subcategory C of modules is said to be Jordan recoverable if a module X in C can be recovered from the Jordan forms, at each vertex, of a generic nilpotent endomorphism. This data is encoded by a tuple of integer partitions.

After we have introduced some definitions and set the context, the main aim of the talk is to explain the notion of Jordan recoverability through various examples, and to highlight a combinatorial characterization of when that property holds for some special subcategories of modules. This result is extending the work of Garver, Patrias and Thomas in Dynkin types. If time allows, we may discuss some open questions related to this result and, in particular, exhibit new ideas to characterize all the subcategories of modules that are Jordan recoverable in the A_n case.

This is a part of my Ph.D. work supervised by Hugh Thomas.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections