where... denote the term with ϖ ϖ α α ˙ ˙ β β ˙ ˙ that is similar to the first one. The Lorentz covariant derivative comes from the usual commutator action of the spin-connection part of Ω Ω . The term with the vierbein results from the π π -automorphism that flips the sign of the AdS-translations and produces anti-commutator h α α α α ˙ ˙ { P α α α α ˙ ˙ , ∙ ∙ } ⋆ ⋆ .