Abstract
There exists a construction of hyperbolic complex Lorentz frames for any signature η. We prove GL(4, R) to be locally isomorphic to U(η, H) by Lie algebra theory. Therefore, the local GL(4, R) gauge symmetry of hyperbolic complex metric g in the nonsymmetric gravitational theory, in fact, is a symmetry of rotations of the hyperbolic complex Lorentz frames.
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