Representation dimension and separable equivalence
Algebra and Geometry Seminar
8th November 2017, 2:30 pm – 3:30 pm
Howard House, 4th Floor Seminar Room
The representation dimension of an algebra is a finite integer that indicates the complexity of the algebra's module category. This dimension was first introduce by Auslander in 1971 and is, in general, notoriously hard to compute. This measure is loosely related to the representation type of an algebra: an algebra has finite representation type if and only if it's representation dimension is less than 3.
Separable equivalence is an equivalence relation on finite dimensional algebras. Over a field of a characteristic p, a group algebra is separably equivalent to the group algebra of its Sylow p-subgroup. We use this relationship between a group and its Sylows to put an upper bound on the representation dimension of any group with a elementary-abelian Sylow subgroup.