# Irreducible decomposition of products of 10D chiral sigma matrices ☆

## Description

Abstract We review the enveloping algebra of the 10-dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the multiplication of the sigma matrices down to linear combinations of irreducible elements. We are able to quickly derive several identities that are not restricted to traces. A copy of the program written in the Mathematica language is provided for the community. ... Title of program: SigmaVector10D.m Catalogue Id: ADNT_v1_0 Nature of problem Products of 10D chiral sigma matrices are calculated and irreducible sums are produced. The program takes advantage of the identity matrices and all possible contractions of the ten-dimensional epsilon tensor with itself to produce results. Several user-implementable rules are included to reduce output and to take the dual of p-forms. The code knows the difference between commuting and non-Abelian elements. Versions of this program held in the CPC repository in Mendeley Data ADNT_v1_0; SigmaVector10D.m; 10.1016/S0010-4655(00)00251-4 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)