There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric 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 relations satisfied by the defining and adjoint representation matrices of SU(N). A few relations special to the case of N=3 are highlighted.

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SU（N）的定义和伴随表示中生成器之间的有用关系

SU（N）的定义和伴随表示中的生成器之间存在许多关系。这些包括Casimir算符，发电机乘积痕迹的公式等。由于存在SU（N）Lie代数研究中出现的完全对称张量$ d_ {abc} $，因此还可以考虑以下关系：包含伴随表示矩阵$（D ^ a）_ {bc} = d_ {abc} $。在本文中，我们总结了SU（N）的定义和伴随表示矩阵所满足的许多有用关系。N = 3情况下的一些特殊关系突出显示。