Abstract
This paper attempts to provide a comprehensive compilation of results, many new here, involving the invariant totally antisymmetric tensors (Omega tensors) which define the Lie algebra cohomology cocycles of su (n), and that play an essential role in the optimal definition of Racah–Casimir operators of su (n). Since the Omega tensors occur naturally within the algebra of totally antisymmetrized products of λ-matrices of su (n), relations within this algebra are studied in detail, and then employed to provide a powerful means of deriving important Omega tensor/cocycle identities. The results include formulas for the squares of all the Omega tensors of su (n). Various key derivations are given to illustrate the methods employed.
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