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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2012 Volume 172, Number 1, Pages 100–121 (Mi tmf6923)

This article is cited in 4 papers

Classical $r$-matrices of two- and three-dimensional Lie superbialgebras and their Poisson–Lie supergroups

A. Eghbali, A. Rezaei-Aghdam

Department of Physics, Faculty of Science, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract: 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, Poisson–Lie supergroup, classical $r$-matrix.

Received: 18.06.2011
Revised: 13.09.2011

DOI: 10.4213/tmf6923


 English version:
Theoretical and Mathematical Physics, 2012, 172:1, 963–986

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