Invariant tensors and Casimir operators for simple compact Lie groups

Abstract

The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing non-primitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.

11 pages, LaTeX, minor changes, version in J. Math. Phys

References in corpus (2)

• Invariant tensors for simple groups
• Higher-order simple Lie algebras

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