Exterior calculus with d 3=0 on two-dimensional quantum plane

In this paper, we construct the algebra of differential forms with exterior differential satisfying d 3 =0 on the two-dimensional quantum plane assuming that the homomorphism defining first-order differential calculus is linear in variables. Assuming d 2 ≠0, we introduce the second-order differentials d 2 x i . The commutation relations between the generators x i , dx i , and d 2 x i of the algebra of differential forms, among dx i , and among d 2 x i , as well as between noncommutative derivatives with generators, are found. The consistency conditions are described.