Irreducible decomposition of products of 10D chiral sigma matrices

We review the enveloping algebra of the 10-dimensional chiral sigma matrice s. To facilitate the computation of the product of several chiral sigma mat rices we have developed a symbolic program. Using this program one can redu ce 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 Mathema tica language is provided for the community. (C) 2001 Elsevier Science B.V. All rights reserved.