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

Howard E. Haber

SciPost Phys. Lect. Notes 21 (2021) · published 20 January 2021

- doi: 10.21468/SciPostPhysLectNotes.21
- Submissions/Reports

### Abstract

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.

### Cited by 9

### Author / Affiliation: mappings to Contributors and Organizations

See all Organizations.-
^{1}Howard Haber

Funder for the research work leading to this publication