From: Subject: Quantum supergroup structure of (1+1)-dimensional quantum superplane Date: Fri, 8 May 2009 22:46:46 -0500 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C9D02E.DDA87E90" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3350 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C9D02E.DDA87E90 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.iop.org/EJ/abstract/0305-4470/34/16/308 Quantum supergroup structure of (1+1)-dimensional = quantum superplane
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Quantum supergroup structure of (1+1)-dimensional = quantum=20 superplane, its dual and its differential calculus

M El = Falaki et=20 al 2001 J. Phys. A: Math. = Gen. 34 3403-3412   doi: 10.1088/0305-4470/= 34/16/308 =20

   PDF= =20 (92 KB) | G= zipped=20 PS (97.8 KB) | References

M=20 El Falaki1,2 and E=20 H Tahri1,3
1=20 Laboratoire de Physique Th=E9orique, Facult=E9 des Sciences, = Universit=E9 Mohamed V,=20 Av. Ibn Battota BP. 1014, Rabat, Morocco
2 Abdus Salam=20 International Centre for Theoretical Physics, Trieste, = Italy
3=20 Permanent address: Laboratoire de Physique Th=E9orique et de Particules, = Facult=E9=20 des Sciences, Universit=E9 Mohammed I, BP. 524, 60000 Oujda, = Morocco.
E-mail:=20 mantrach@fsr.ac.ma and tahrie@sciences.univ-ouj= da.ac.ma

Abstract. We = show that the=20 (1+1)-dimensional quantum superplane introduced by Manin is a quantum=20 supergroup, according to the Faddeev-Reshetikhin-Takhtajan approach, = when it is=20 extended by the inverse of the bosonic variable. We then give its = supermatrix=20 element, its corresponding R-matrix and its Hopf structure. This = new=20 point of view allows us, first, to realize its dual Hopf superalgebra = starting=20 from postulated initial pairings. Second, we construct a right-invariant = differential calculus on it and then deduce the corresponding quantum = Lie=20 superalgebra which as a commutation superalgebra appears classical, and = as Hopf=20 structure is a non-cocommutative q-deformed one.

PACS numbers: 0220, 0365F, 1130P

Print publication: Issue 16 (27 April=20 2001)
Received 4 October 2000, in final = form 2=20 February 2001

Post=20 to CiteUlike | Post=20 to Connotea | Post=20 to Bibsonomy

 

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