Coxeter groups, path algebras and preprojective algebras (NAGRT)
MSRI: Simons Auditorium
To a finite acyclic quiver we can associate a path algebra kQ (k a field), a preprojective algebra and a Coxeter group. Using a natural map from the Coxeter group to ideals in the preprojective algebra,investigated in work with Buan, Iyama and Scott, we establish a 1-1 correspondence between elements in the Coxeter group and cofinite quotient closed subcategories of the finite dimensional kQ-modules. This is based on work with Oppermann and Thomas.