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

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)摘要 我们提出一款计算机程序，用于生成并求解任意型李代数（Lie algebra）及其表示的保持分次（grading）收缩的定义方程。该算法适用于任意有限阿贝尔分次半群，可对分次为一般或非一般的李代数和/或表示执行收缩操作。 程序名称：CONTRACTIONS 目录标识号：ACNN_v1_0 问题概述 在物理学中，收缩过程是关联不同物理系统或理论的对称李群（Lie group）与李代数的一种形式化方法。近期，一种基于保留特定分次的李代数收缩新方法被构建。引入至李代数元素作用中的收缩参数，必须满足一组二次方程，方可定义李代数（或其表示）的收缩。然而在实际操作中，…… 本程序在Mendeley Data的CPC程序库中的版本：ACNN_v1_0；CONTRACTIONS；10.1016/0010-4655(93)90063-I 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019）