Compilation of relations for the antisymmetric tensors defined by the Lie algebra cocycles of $su(n)$
de Azcárraga, J. A. ; Macfarlane, A. J.
arXiv, 0006026 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-06-27
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Mathematics - Representation Theory 
@article{0006026,
     author = {de Azc\'arraga, J. A. and Macfarlane, A. J.},
     title = {Compilation of relations for the antisymmetric tensors defined by the
  Lie algebra cocycles of $su(n)$},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0006026}
}

de Azcárraga, J. A.; Macfarlane, A. J. Compilation of relations for the antisymmetric tensors defined by the
  Lie algebra cocycles of $su(n)$. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0006026/