GAUGE FORMULATION OF THE SPINNING BLACK-HOLE IN (2-DIMENSIONAL ANTI-DE SITTER SPACE(1))

We compute the group element of SO(2,2) associated with the spinning b lack hole found by Banados, Teitelboim, and Zanelli in (2 + 1)-dimensi onal anti-de Sitter space-time. We show that their metric is built wit h SO(2,2) gauge invariant quantities and satisfies Einstein's equation s with a negative cosmological constant. Moreover, although the metric is singular on the horizons, the group element is continuous and poss esses a kink there. We also consider the extremal configurations and t he Poincare limit as special cases.