LieART—A Mathematica application for Lie algebras and representation theory

Published: 01-01-2015| Version 1 | DOI: 10.17632/6zyr73d62r.1
Robert Feger,
Thomas W. Kephart


This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract We present the Mathematica application “LieART” (Lie Algebras and Representation Theory) 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 st... Title of program: LieART Catalogue Id: AEVL_v1_0 Nature of problem The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebas. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This co ... Versions of this program held in the CPC repository in Mendeley Data AEVL_v1_0; LieART; 10.1016/j.cpc.2014.12.023 AEVL_v1_0; LieART; 10.1016/j.cpc.2014.12.023