Tuesday, October 15, 16:00, 7.527.

Kevin Schlegel
The second Brauer-Thrall conjecture for subcategories

Abstract:
The second Brauer-Thrall conjecture states that a finite dimensional algebra over an infinite field is either of finite or strongly unbounded representation type. We extend the conjecture to certain subcategories of the module category and approach it through generic modules. It is shown that the newly formulated conjecture holds true for finite dimensional algebras over algebraically closed fields under the assumption that the Krull-Gabriel dimension of the algebra is defined.