Tuesday, November 20, 15:15, 7.527
Jorge Vitoria (City U London)
Quantity and size: Auslander-type results in silting theory
A famous theorem of Auslander states that a finite dimensional algebra is of
finite representation type if and only if every module is additively
equivalent to a finite dimensional one. This establishes a correlation
between quantity (of indecomposable finite dimensional modules) and size (of
We will discuss the ocurrence of an analogous correlation in silting theory.
Indeed, for a finite dimensional algebra A we prove that
1) A is \tau-tilting finite if and only if every silting module is
additively equivalent to a finite dimensional one.
2) A is silting discrete if and only if every bounded silting complex is
additively equivalent to a compact one.
This is based on joint work with L. Angeleri Hügel and F. Marks and on
ongoing joint work with L. Angeleri Hügel and D. Pauksztello.