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This paper deals with the striking fact that there is an essentiallycanonical path from the $i$-th Lie algebra cohomology cocycle, $i=1,2,... l$,of a simple compact Lie algebra $\g$ of rank $l$ to the definition of itsprimitive Casimir operators $C^{(i)}$ of order $m_i$. Thus one obtains acomplete set of Racah-Casimir operators $C^{(i)}$ for each $\g$ and nothingelse. The paper then goes on to develop a general formula for the eigenvalue$c^{(i)}$ of each $C^{(i)}$ valid for any representation of $\g$, and therebyto relate $c^{(i)}$ to a suitably defined generalised Dynkin index. The form ofthe formula for $c^{(i)}$ for $su(n)$ is known sufficiently explicitly to makeclear some interesting and important features. For the purposes ofillustration, detailed results are displayed for some classes of representationof $su(n)$, including all the fundamental ones and the adjoint representation.Comment: Latex, 16 page

Optimally defined Racah–Casimir operators for su(n) and their eigenvalues for various classes of representations