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

@article{Haber2019UsefulRA,
  title={Useful relations among the generators in the defining and adjoint representations of SU(N)},
  author={Howard E. Haber},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
  • H. Haber
  • Published 31 December 2019
  • Mathematics
  • arXiv: Mathematical Physics
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… 
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