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

M. El Falaki·E. H. Tahri
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Abstract

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

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M. El Falaki, E. H. Tahri. 1999-10-15. Quantum supergroup structure of the 1+1-dimensional quantum superplane, its dual and its differential calculus. https://arxiv.org/abs/math-ph/9910024

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