Killing – An algebraic computational package for Lie algebras

Published: 01-01-2000| Version 1 | DOI: 10.17632/82yy4xkk6j.1
Esmerindo de Sousa Bernardes


Abstract The Killing package is a set of algebraic computational procedures to manipulate elements of representation theory for classical, exceptional and deformed Lie algebras. It is divided in two major parts: (1) The Roots & Weights formalism to classify all semisimple Lie algebras and their irreducible representations, and (2) The Gelfand–Tsetlin method to construct explicitly the irreducible representations of classical Lie algebras, including the deformed unitary Lie algebras. Title of program: KILLING Catalogue Id: ADLX_v1_0 Nature of problem Symmetry has been a very important fundamental principle underlying human knowledge about our physical world. Among several mathematical formulations of symmetry, the Lie algebras and their corresponding Lie groups are probably the ones most explored. They were discovered by Sophus Lie and Wilhelm Killing during the last two decades of the 19th century. Lie's work on Lie groups was inspired by Galois' work in 1832 in which he discovered the finite groups. Independently, Killing had started a cla ... Versions of this program held in the CPC repository in Mendeley Data ADLX_v1_0; KILLING; 10.1016/S0010-4655(00)00006-0 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)