SUNY at Stony Brook MAT 641: Quiver representations
Fall 2008

Welcome to MAT 641: Quiver representations

Date and time: MWF 9:35am-10:30am in Physics P117 MW 10-11:20 in Math P-131.

Planned topics:

  1. Basic notions of quiver representations. Path algebra, etc.
  2. Gabriel's theorem. Reflection functors.
  3. Hall algebra and construction of basis in universal enveloping algebra from quiver representations
  4. Quiver varieties (Nakajima, Lusztig)
  • Basic homological algebra (Ext functors)
  • Basic algebraic geometry (notion of algebraic variety, sheaf)
  • Familiarity with root systems and semisimple Lie algebras (optional)
Familiarity with the notion of derived category would be quite helpful, but not required (I will give a brief review).