# The computer calculation of graded contractions of Lie algebras and their representations

## Description

Abstract We present a computer program to generate and solve the defining equations for grading preserving contractions of Lie algebras of any type, and their representations. The algorithm applies to any grading semi-group which is finite and Abelian. It can perform contractions of Lie algebras and/or representations for which the grading is either generic or not. Title of program: CONTRACTIONS Catalogue Id: ACNN_v1_0 Nature of problem In physics, the contraction procedure appears as a formal way to relate the symmetry Lie groups (Lie algebras) of different physical systems, or theories. A new method for contracting Lie algebras, based on the preservation of some grading, was recently constructed. The contraction parameters introduced into the action of the elements of the Lie algebra must satisfy some system of quadratic equations in order to define a contraction of Lie algebra (or its representations). However, in practice s ... Versions of this program held in the CPC repository in Mendeley Data ACNN_v1_0; CONTRACTIONS; 10.1016/0010-4655(93)90063-I This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)