Kayla Wright - A Geometric Model for Semilinear Locally Gentle Algebras

Abstract: In joint work with Esther Banaian, Raphael Bennett-Tennenhaus, and Karin Jacobsen, we define a geometric model for certain generalizations of gentle algebras. We consider semilinear locally gentle algebras - (potentially infinite-dimensional) gentle algebras where we allow division rings on vertices and we associate automorphisms of these division rings to each arrow with certain multiplication rules. In this talk, we will demonstrate how one can utilize topological tools to visualize objects in the module category for such algebras. Classically, it has been shown that one can model various quiver algebras and associated categories using surfaces. In the simplest example, the category of indecomposable type A quiver representations can be viewed using triangulations of polygons. For our case, we model our algebras with punctured surfaces that have been cut up and stitched back together at the seams. This process of cutting and stitching the surface is a geometric realization of an algebraic result of Zembyk and it allows us to endow an existing geometric model for locally gentle algebras with a semilinear twist.