Characterization of 2-cocycles and 2-coboundaries on Direct Sum of Banach Algebras

Let A and B be Banach algebras. In this paper, we investigate the structure of 2-cocycles and 2-coboundaries on A⊕B, when A and B are unital. Actually, we provide a specific criterion for each 2-cocycle map and establish a connection between 2-cocycles and 2-coboundaries on A ⊕ B and 2-cocycles and 2-coboundaries on A and B. Finally, our results lead to a connection between H2(A, A∗),H2(B, B∗) and H2(A ⊕ B, A∗ ⊕ B∗).