Pointers to software for algebras and groups.
On this page we provide links to useful software for Lie algebras, algebras,
groups, representation theory
and related topics. This page is part of the web-pages for the book
Symmetries, Lie algebras and representations
( Cambridge University
Press ) by
Jürgen Fuchs and
Christoph Schweigert .
- CHEVIE is a computer algebra package for symbolic
calculations with generic character tables of groups of Lie type, Weyl groups
and Hecke algebras. It is based on the computer algebra systems GAP and Maple.
is a package of programs to work with particular classes of finite-dimensional
algebras and some combinatorial aspects of their finite-dimensional
(Groups, Algorithms, and Programming) is a system for computational discrete
algebra, with particular emphasis on computational group theory. GAP contains
e.g. routines for dealing with Weyl groups and Hecke algebras. For more
information see the
- Special routines in GAP allow to perform calculations for
Weyl Groups and Hecke Algebras.
is a C program designed to perform calculations with twisted and untwisted
affine Lie algebras, including e.g. the Kac-Peterson formula for the modular
matrix S and applications to coset conformal field theories. kac has most
functionalities of wei, but it has no function to compute the weight system of
a finite-dimensional irreducible representation of a finite-dimensional
simple Lie algebra. You can download kac from its
homepage. Its author
is Bert Schellekens
(NIKHEF, Amsterdam, The Netherlands).
is a software system for calculations in Lie algebras. It focuses on the
representation theory of complex semisimple and reductive Lie algebras
(allowing e.g. for the computation of tensor product decompositions), and on
the structure of their Weyl groups and root systems. It includes such features
as branching rules, Bruhat ordering and Kazhdan-Lusztig polynomials.
- There is also an unofficial variant called LiEGAP which is callable from GAP.
- LIE (REDUCE package)
is also the name of a REDUCE package of functions for the classification
of real n-dimensional Lie algebras.
Magma is designed to solve computational problems in algebra,
number theory, geometry and combinatorics. Magma provides a mathematical
environment for computing with algebraic and algebraic-geometric objects.
- In the Maple Share library which is distributed with more recent
releases of Maple, there are the packages
coxeter and weyl.
The coxeter package allows to deal with root systems,
reflection groups and characters, while the weyl
package contains procedures for manipulating weight vectors and
computing weight multiplicities for irreducible representations of semisimple
- There is an online
for coxeter and weyl. The packages can be obtained by anonymous
Anonymous ftp distribution sites for the Maple share library are
- There is a Mathematica program lie, available in the
which allows to construct solutions of many linear and also non-linear (systems of)
differential equations by making use of an underlying Lie algebra structure.
is a Mathematica program which allows to determine the symmetries of
(ordinary and partial, linear and nonlinear) differential equations. One can
also obtain the algebraic properties of the related Lie algebra,
differential representations of the Lie algebra, etc.
- Schur is an interactive program
that can be used to calculate branching rules, Kronecker products, fusion rules
of WZW theories, Casimir invariants, dimensions, Young diagrams and their hook
lengths etc. Its algorithms are based on the theory of partitions (which underlies
the representation theory of the symmetric group), and in particular on Schur
is a Macintosh application that performs standard computations in simple Lie
algebras and their finite dimensional representations over the complex numbers.
For such representations, the software computes weight multiplicities,
branching rules, tensor product decompositions etc. Version two of simpLie
includes various extensions such as elements of finite order (EFO's), coset
graphs and quasicrystals.
- Symmetrica is a computer algebra package
devoted to representation theory, invariant theory and combinatorics of finite
symmetric groups and related classes of groups.
- wei is a Fortran 77 program that computes dimensions and
weight systems of irreducible representations of finite-dimensional simple Lie
algebras, tensor product decompositions of such representations, and also the
corresponding fusion rules of WZW theories, and quantum dimensions.
To obtain it, send a mail
to Jürgen Fuchs.
Other useful links can be found at the server of
CAN in Amsterdam, or at the server of
Return to the home page of the book.
Last modified: 1 April 2002