Abstract
The fourth-order indices for Lie algebras have been defined and studied by Patera, Sharp, and Winternitz. We show that it may be more convenient to modify the original definition and that the modified fourth-order indices are intimately related to eigenvalues of symmetrized fourth-order Casimir invariants. Explicit expressions for these quantities are given and we also find a quartic trace identity involving the generic element of these Lie algebras. We discuss the triality principle for the Lie algebra D4 in connection with identical vanishing of the modified fourth-order index for this algebra.
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