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Representation theory of EI-categories
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
5.4.1 Relation to recollements
5.4.2 A non-trivial example
6 Outlook
References
Dissertation
Representation theory of EI-categories / Karsten Dietrich
Entstehung
2010
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