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

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dc.creatorFalaki, M. El
dc.creatorTahri, E. H.
dc.date1999-10-15
dc.date.accessioned2026-07-07T04:33:00Z
dc.date.available2026-07-07T04:33:00Z
dc.descriptionWe 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.
dc.description15 pages, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/9910024
dc.identifierhttp://arxiv.org/abs/math-ph/9910024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58413
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subject17B37
dc.titleQuantum supergroup structure of the 1+1-dimensional quantum superplane, its dual and its differential calculus
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