Breadcrumb
Representation of quivers
Supervisor: Aidan Schofield
Theme: Representation Theory
This project centres on the representation of quivers. A quiver is a set
of vertices together with a set of arrows between these vertices, and a representation of a quiver is just a way of assigning a vector space to each vertex of the quiver, and a linear map to each arrow. To give a simple example: the quiver might have a single vertex and a single arrow going
from that vertex to itself; in this case a representation is just a vector space together with a linear endomorphism. It turns out that many classification problems in mathematics can be reduced to studying representations of a quiver. The techniques used in the study of representations of quivers involve many geometric ideas, such as the
study of orbits of groups acting on vector spaces. This is the subject of geometric invariant theory.