Abstract
The so-called Gell-Mann formula expresses the Lie algebra elements in terms of the corresponding Inönü–Wigner contracted ones. In the case of sl(n, ℝ) and su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is generally not valid, and applies only in the cases of some algebra representations. A generalization of the Gell-Mann formula for sl(5, ℝ) and su(5) algebras, that is valid for all representations, is obtained in a group manifold framework of the SO(5) and/or Spin(5) group. Matrix elements of the sl(5, ℝ) noncompact operators, relevant for Affine Gauge Gravity and four-branes, are obtained for an arbitrary irreducible representation.
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