Geodesic
Classical $r$-matrices of two- and three-dimensional Lie superbialgebras and their Poisson--Lie supergroups
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 100-121

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We obtain the classical $r$-matrices of two- and three-dimensional Lie superbialgebras. We thus classify all two- and three-dimensional coboundary Lie superbialgebras and their types (triangular, quasitriangular, or factorable). Using the Sklyanin superbracket, we then obtain the super Poisson structures on the related Poisson–Lie supergroups.
Keywords: Lie superbialgebra, classical $r$-matrix.
Mots-clés : Poisson–Lie supergroup 
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     title = {Classical $r$-matrices of two- and three-dimensional {Lie} superbialgebras and their {Poisson--Lie} supergroups},
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A. Eghbali; A. Rezaei-Aghdam. Classical $r$-matrices of two- and three-dimensional Lie superbialgebras and their Poisson--Lie supergroups. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 100-121. http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a6/