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There are numerous relations among the generators in the defining and adjointrepresentations of SU(N). These include Casimir operators, formulae for tracesof products of generators, etc. Due to the existence of the completelysymmetric tensor $d_{abc}$ that arises in the study of the SU(N) Lie algebra,one can also consider relations that involve the adjoint representation matrix,$(D^a)_{bc}=d_{abc}$. In this review, we summarize many useful relationssatisfied by the defining and adjoint representation matrices of SU(N). A fewrelations special to the case of N=3 are highlighted.

Useful relations among the generators in the defining and adjoint representations of SU(N)