GroupMath: A Mathematica package for group theory calculations

Abstract

GroupMath is a Mathematica package which performs several calculations related to semi-simple Lie algebras and the permutation groups, both of which are important in particle physics as well as in other areas of research.

arXiv commentDescribes version 1.1 of the program. Code available on http://renatofonseca.net/groupmath

References in corpus (13)

• SARAH 4: A tool for (not only SUSY) model builders
• $SU(3)\otimes U(1)$ Model for Electroweak Interactions
• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory
• PyR@TE: Renormalization Group Equations for General Gauge Theories
• PyR@TE 3
• Enumerating the operators of an effective field theory
• Calculating the renormalisation group equations of a SUSY model with Susyno
• Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building
• The Sym2Int program: going from symmetries to interactions
• On the chirality of the SM and the fermion content of GUTs
• Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8
• Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras
• Renormalization in supersymmetric models

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