The subject of this summer semester's algebra seminar will be quivers and their representations. A quiver is a finite directed graph, and we call "quiver representation" the assignment of a vector space to each vertex and a linear map to each arrow. The focal point of the seminar is the fact that the representations of a finite-dimensional algebra (over an algebraically closed field) can be encoded and understood through the representations of these simple combinatorial objects (quivers). Our main goal is to give an account of Gabriel's theorem, which characterizes quivers of finite orbit type. These are quivers that have only finitely many isomorphism classes of representations in any prescribed dimension. We will follow Ralf Schiffler's book on quiver representations.
The seminar will be offered as a block seminar, taking place on two Saturdays: 13th May and 17th June. All talks will take place in SeMath (Pontdriesch 10-16, Room 008). This seminar is aimed at both bachelor and master students, and the pre-requisites for participation are only linear algebra I and II. All other information concerning the seminar will be provided in the learning room in RWTHmoodle.