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

M El Falaki et
al 2001 J. Phys. A: Math. Gen. 34 3403-3412   doi: 10.1088/0305-4470/34/16/308

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M
El Falaki1,2 and E
H Tahri1,3
1
Laboratoire de Physique Théorique, Faculté des Sciences, Université Mohamed V,
Av. Ibn Battota BP. 1014, Rabat, Morocco
2 Abdus Salam
International Centre for Theoretical Physics, Trieste, Italy
3
Permanent address: Laboratoire de Physique Théorique et de Particules, Faculté
des Sciences, Université Mohammed I, BP. 524, 60000 Oujda, Morocco.
E-mail:
[email-masked] and [email-masked]

Abstract. We show that the
(1+1)-dimensional quantum superplane introduced by Manin is a quantum
supergroup, according to the Faddeev-Reshetikhin-Takhtajan approach, when it is
extended by the inverse of the bosonic variable. We then 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 superalgebra appears classical, and as Hopf
structure is a non-cocommutative q-deformed one.

PACS numbers: 0220, 0365F, 1130P

Print publication: Issue 16 (27 April
2001)
Received 4 October 2000, in final form 2
February 2001

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