(-1)-weak amenability of second dual of real banach algebras

Let (a,∥⋅∥) be a real banach algebra, a complex algebra ac be a complexification of a and ∥|⋅∥| be an algebra norm on ac satisfying a simple condition together with the norm ∥⋅∥ on a. in this paper we first show that a∗ is a real banach a∗∗-module if and only if (ac)∗ is a complex banach (ac)∗∗-module. next we prove that a∗∗ is (−1)-weakly amenable if and only if (ac)∗∗ is (−1)-weakly amenable. finally, we give some examples of real banach algebras which their second duals of some them are and of others are not (−1)-weakly amenable.