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 RacahCasimir operators of su(n). Since the Omega tensors occur naturally within the algebra of totally antisymmetrized products of λmatrices 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.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2001
 DOI:
 10.1142/S0217751X01003111
 arXiv:
 arXiv:mathph/0006026
 Bibcode:
 2001IJMPA..16.1377D
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Representation Theory
 EPrint:
 Latex file (run thrice). Misprints corrected, Refs. updated. Published in IJMPA 16, 13771405 (2001)