Compilation of relations for the antisymmetric tensors defined by the Lie algebra cocycles of $su(n)$

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 antisymmetrised products of $\lambda$-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.

Latex file (run thrice). Misprints corrected, Refs. updated. Published in IJMPA 16, 1377-1405 (2001)

References in corpus (4)

• On characteristic equations, trace identities and Casimir operators of simple Lie algebras
• Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras
• Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations
• Fermionic realisations of simple Lie algebras

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