Combinatorial REPresentation Theory

CREP is a package of programs to work with particular classes of finite-dimensional algebras (e.g. completely separating algebras, hereditary algebras) resp. related structures (e.g. unit forms, partially ordered sets) and some combinatorial aspects of their finite-dimensional representations (e.g. dimension vectors, Tits and Euler forms, thin modules, postprojective, preinjective and tubular Auslander-Reiten components). Moreover there are data bases containing some important classifications (e.g. tame concealed algebras, sincere representation-directed algebras, minimal wild concealed algebras).

The crep package

CREP provides a variety of functions and data related to the representation theory of finite-dimensional algebras

The esrd package

the esrd package is a supplement to CREP containing functions and data about the exceptional sincere representation directed algebras

The get_alg interface

the functions described in this section provide means of graphical display and graphical input for most types of algebras that currently can be handled by the various packages of the CREP system

The hall_e8 package

the hall_e8 package is a supplement to CREP containing a data base and access functions about Hall polynomials for an algebra of type E₈

The heralg package

the heralg package is a supplement to CREP dealing with hereditary algebras

The nor package

the nor package is a supplement to CREP for counting representations over small quivers

The repetit package

the repetit package is a supplement to CREP containing functions and data about repetitive algebras and iteratedly tilted algebras of type E₆, E₇ and E₈

The tpe package

the tpe package is a supplement to CREP containing functions and data about completely separating tame poset algebras containing algebras of type E^~₆, E^~₇ and E^~₈

The tubular package

the tubular package contains functions dealing with K-theoretic methods for canonical algebras and weighted projective lines with special emphasis on tubular canonical algebras and the evaluation of "telescoping functors"

The uforms package

the uforms package contains functions dealing with unit forms

The ufstrong package

the ufstrong package contains functions dealing with "strong" properties of unit forms

The xpre function family

the function xpre looks for and constructs preprojective components of a given algebra. Compared to the function preproj of the main package of crep, which performs a similar task, the function xpre is much more general with respect to the algebras it accepts. In addition it comes with its own graphical interface.

The xpreproj interface

the xpreproj function provides a graphical front end for the function xpreproj of the main package of CREP