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We show that the 1+1-dimensional quantum superplane introduced by Manin is aquantum supergroup according to the Faddeev-Reshetikhin-Takhtajan approach. Wegive its supermatrix element, its corresponding R-matrix and its Hopfstructure. This new point of view allows us, first, to realize its dual Hopfsuperalgebra starting from postulated initial pairings. Second, we construct aright-invariant differential calculus on it and then deduce the correspondingquantum Lie superalgebra which as a commutation super-algebra appearsclassical, and as Hopf structure is a non-cocommutative q-deformed one. Anisomorphism between the latter and the dual one obtained in the first method isgiven.

Quantum supergroup structure of (1+1)-dimensional quantum superplane, its dual and its differential calculus