For many applications even the algebra itself may be assumed to be of finite dimension over k. Popular examples for algebras of this kind are the group algebras for finite groups or the finite-dimensional factor algebras of polynomial algebras.
If one wants to approach categories with finite-dimensional morphism spaces, the language of quivers is an appropriate way. Recall that quiver is a shorthand for directed graph with possibly multiple edges and loops. This is a purely combinatorial object inviting to computational access.
The aim of CREP is to provide algorithms using this access for research and teaching. The system is being designed along the lines of current research. On the other hand, there are many basic functions and, in particular. graphical interfaces which are instructive and useful for students and neophytes.
The code of CREP is freely available. People are invited to contribute.
The CREP development group in Bielefeld consists of several researchers and students led by Peter Dräxler. There is intensive collaboration with colleagues at universities in Bayreuth, Berlin, Chemnitz, Düsseldorf, Essen, Kiew, Mexico, Paderborn, München and Torun. This is reflected by the contents of Part 2 and Part 3 of the CREP manual containing various contributations and packages from these places.
CREP is not yet a general purpose system but rather specific. It has proved to be efficient for various important questions which appear in the present research about representations of algebras. The vision is to accumulate more and more routines in order to obtain a helpful and general system for representation theory and related topics.
The programs of CREP are written in Pascal, C, Java, and in the Maple programming language. Nevetheless, the user will only see a package of Maple routines. Thus she/he only has to learn how to use Maple and to understand the data structures of the input and output. In particular, she/he can refer to convenient help pages explaining all procedures. In version 1.3 also a graphical input and output routine was included which is based on XForms.
Some (non interactive) example pages how working with CREP looks like.
There is also an interactive version of the function xpre searching for and constructing preprojective components of an algebra, whose input and output have been adapted to use via a web browser. (This will need Java 1.1.)
Parts 1 - 4 of the printed manual are available as volumes E96-002, E97-009, E99-007, and E00-005 of the SFB 343.
A short introduction to the mathematical background of CREP is presented in
P. Dräxler, R. Nörenberg:
Classification problems in the combinatorial representation theory of finite-dimensional algebras
Computational methods for representations of groups and algebras,
(edited by P. Dräxler, G.O. Michler, C.M. Ringel),
Progress in Mathematics 173 (1999), 3-28
Additional material on computational aspects in the representation theory of algebras can be found in the references of the paper by P. Dräxler and R. Nörenberg. Moreover, an introductory book on the subject is in preparation.
Running CREP will require the Maple system to be present, preferably MapleV release 3 or later. Usually for the installation Pascal and C compilers will be needed.