lieart is hosted by Hepforge, IPPP Durham


LieART (Lie Algebras and Representation Theory) is a Mathematica application for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix of the associated publication.

LieART is associated with arXiv:1206.6379 [math-ph]


Automatic Installation

Start Mathematica and in the front end select the menu entry FileInstall.. In the appearing dialog select Application as Type of Item to Install and the tar.gz file in the open file dialog from Source. (It is not necessary to extract the tar.gz archive since Mathematica does this automatically.) Choose whether you want to install LieART only for an individual user or system wide. For a system-wide installation you might be asked for the superuser password.

Manual Installation

The above procedure in Mathematica 7 only allows to automatically install the Mathematica package file (LieART.m) of LieART without the documentation. We therefore suggest the manual installation of the LieART application in Mathematica 7 and in Mathematica 8 through 10 if problems with the automatic installation occur.

Extract the archive to the subdirectory AddOns/Applications of the directory to which $UserBaseDirectory is set for a user-only installation. For a system-wide installation place it in the according subdirectory of $InstallationDirectory. Restart Mathematica to allow it to integrate LieART's documentation it its help system.


The documentation of LieART is integrated in Mathematica's help system. After restarting Mathematica the following path leads to LieART's documentation:

HelpDocumentation Center Add-Ons & Packages (at the bottom) → LieART, Button Documentation

(Alternatively, a search for LieART (with correct case) in the Documentation Center leads to the same page.) The displayed page serves as the documentation home of LieART and includes links to the descriptions of its most important functions.

The documentation of LieART includes a Quick Start Tutorial, which can be found almost at the bottom of LieART's documentation home under the section Tutorials.

Tables of representation properties, tensor products and branching rules generated by LieART can be found in the section Tables at the bottom of LieART's documentation home.

LaTeX Package

LieART comes with a LaTeX package that defines commands to display irreps, roots and weights properly. The style file (lieart.sty) can be found in the subdirectory latex/ of the LieART project tree. Please copy it to a location where your LaTeX installation can find it.


In case of questions or problems with LieART or for bug reporting please send an email to robert.feger(at)


Copyright (C) 2012-2014 Robert Feger

This application is subject to the GNU Lesser General Public License (LGPL). For details see COPYING and COPYING.LESSER that come with the application.