The 1 + 1-dimensional quantum superplane introduced by Manin is shown to be a quantum supergroup according to the Faddeev-Reshetikhin-Takhtajan approach. Its supermatrix element, the corresponding R-matrix and Hopf structure are calculated. This approach allows one to realize the dual Hopf superalgebra of this quantum supergroup starting from postulated initial pairings. The authors also construct a right-invariant differential calculus for such quantum superplane structures , and then derive the corresponding quantum Lie superalgebra which is defined in this paper as a commutation superalgebra that appears as a classical structure, whereas when defined as a Hopf algebra structure it is a non-cocommutative q-deformed algebra. Duality is also considered for such quantum superalgebras.
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http://www.iop.org/EJ/abstract/0305-4470/34/16/308
http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Amath-ph%
