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We study the field equations of the Plebanski action for general relativitywhen both the cosmological constant and an Immirzi parameter are present. Weshow that the Lagrange multiplier, which usually gets identified with the Weylcurvature, now acquires a trace part. Some consequences of this for a class ofmodified gravity theories recently proposed in the literature are brieflydiscussed.

A note on the Plebanski action with cosmological constant and an Immirzi parameter