Jan Schröer

FD-Literature


My aim is to provide a list of references for people who are interested to learn about the representation theory of finite-dimensional algebras, but don't know where to start.
I don't try to give a complete list of publications. I just want to provide a starting point for newcomers. Sometimes I don't mention the original articles and their authors, but rather give preference to a readable survey article which might be written by somebody else.
I made a list of topics mention a couple of articles for each. Of course one can argue that some articles should rather belong to another topic, or to several topics at the same time. Sorry for that.
All parts of this page are under construction.
Your are welcome to send comments and suggestions.
All this is influenced by my personal taste and ignorance.


Text books on representation theory

Unfortunately, there aren't many books containing an introduction to representation theory of algebras. Here are some of them: Back to the top
Text books on quantum groups

There are very interesting connections between representation theory of algebras and the theory of quantum groups and their canonical bases. Here are some books on quantum groups (only occasionally dealing with the mentioned connections): The link to finite-dimensional algebras is obtained via Ringel-Hall algebras. Most of Ringel's articles on this topic are readable and I recommend them as a starting point. Also Reineke's articles on quivers and Ringel-Hall algebras are accessible.
Back to the top
Ringel-Hall algebras Back to the top
Derived categories and tilting theory Back to the top
Geometric aspects of representation theory Back to the top
Auslander-Reiten theory Back to the top
Tame algebras Back to the top
Survey articles Back to the top
Every couple of years there is an ICRA (International Conference on Representations of Algebras). The corresponding conference proceedings contain some fundamental and influential papers.

Here is a (still incomplete) list of ICRA Proceedings. Unfortunately, several are out of print, but you might find them in any good mathematics library... Other conference proceedings: Back to the top
Cluster algebras

There are many publications on cluster algebras and related topics. Most of them you can find here: Fomin's Cluster Algebra Portal Below you find a (not up to date) almost random collection of papers on cluster algebras. I will try to add some comments in the future.
Foundations
Cluster categories (acyclic cluster algebras and beyond)

Roughly speaking, the cluster variables of an acylic cluster algebra correspond to the real Schur roots of an asscoiated Kac-Moody Lie algebra. This belongs to the universe of herditary algebras and tilting theory.
Connections to preprojective algebras, (semi)canonical bases and quiver varieties

The graded dual of the positive part of a universal enveloping algebra of type A,D,E carries a cluster algebra structure. (See Berenstein, Fomin, Zelevinsky: Cluster Algebras III) The cluster variables belong to the dual of Lusztig's semicanonical basis. (See Geiß, Leclerc, Schröer: Rigid modules)
More articles Back to the top

More literature will be added. Please send me your suggestions!