Representation theory of EI-categories / Karsten Dietrich. 2010
Content
- 1 Introduction
- 2 Preliminaries
- 2.1 Definition of EI-categories and examples
- 2.2 Simple and projective modules
- 2.3 Induction and restriction
- 3 EI-categories of finite representation type
- 3.1 Finite representation type for finite groups, quivers and posets
- 3.2 The Gabriel-quiver of a finite dimensional algebra
- 3.3 Covering theory
- 3.4 Relative projectivity, vertices and sources
- 3.5 The endotrivial case
- 3.6 EI-categories with two objects
- 3.6.1 The easiest example
- 3.6.2 The characteristic plays a role
- 3.6.3 Free action implies infinite type
- 3.7 EI-category algebras with two simple modules
- 3.8 Two objects and cyclic automorphism groups
- 4 The finitistic dimension of EI-category algebras
- 5 The finitistic dimension of algebras with a directed stratification
- 5.1 Trivial extensions of abelian categories and finitistic dimension
- 5.2 Basic notions and properties
- 5.3 Projective resolutions and the main result
- 5.4 Relation to known results and examples
- 6 Outlook
- References