MATH 3094: Undergraduate Seminar – Quiver Representations

Instructor: Prof. Ralf Schiffler

Students with an interest in Algebra and Combinatorics may be interested in this Honors seminar. Appropriate for any junior or senior with substantial mathematical background and interest, not just math majors.

A quiver is an oriented graph. A quiver representation is a collection of vector spaces and linear maps; one vector space V_i for each vertex i of the quiver and one linear map f_{ij} from V_i to V_j for each arrow i–>j of the quiver.

The complexity of different representations depends on the quiver. For some (few) quivers we can explicitly write down a finite number of representations such that any representation of the quiver can be constructed from our finite list by taking direct sums and using isomorphisms.  In these cases our finite list can be constructed combinatorially in the so-called Auslander-Reiten quiver.

We will study the properties of quiver representations, and see how to compute the Auslander-Reiten quiver in specific examples, using algebraic methods as well as combinatorial methods for example triangulations of polygons.

Contact Prof. Schiffler with any questions or to request a permission number.