Group theory factors for Feynman diagrams

We present algorithms for the group independent reduction of group theory f actors of Feynman diagrams. We also give formulas and values for a large nu mber of group invariants in which the group theory factors are expressed. T his includes formulas for various contractions of symmetric invariant tenso rs, formulas and algorithms for the computation of characters and generaliz ed Dynkin indices and trace identities. Tables of all Dynkin indices for al l exceptional algebras are presented, as well as all trace identities to or der equal to the dual Coxeter number. Further results are available through efficient computer algorithms.