Algebra and geometry: G-defects: Structures into the wild

  • Date: –17:00
  • Location: Zoom Meeting
  • Lecturer: Michele Del Zotto (Uppsala)
  • Organiser: Matematiska institutionen
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

A classical result in the representation theory of tame algebras is that the module category is the Ringel sum of the projective, the regular, and the injective modules. The subcategory of regular modules is a subcategory controlled by the Dlab-Ringel defect. The regular modules are further organized in standard tubes.

In this talk, after a brief review of the above standard results to fix notations and conventions, we will discuss a generalization of this idea to the module categories of some classes of wild algebras, defined using quivers with potentials.

We will introduce the g-Dlab-Ringel defects, a generalization of the concept of Dlab-Ringel defect, associated to a Lie algebra g. The ordinary Dlab-Ringel defect corresponds to the case g = a_1, in the Cartan classification.

Categories of generalized g-regular modules are defined as the categories controlled by g-Dlab-Ringel defects.

These are structures that might prove useful to organize algebras of wild representation type – that are the vast majority after the Drozd trichotomy theorem.