Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups

Abstract

We obtain the classical r-matrices of two and three dimensional Lie super-bialgebras. We thus classify all two and three dimensional coboundary Lie super-bialgebras and their types (triangular, quasi-triangular, or factorable). Using the Sklyanin superbracket, we then obtain the super Poisson structures on the related Poisson-Lie supergroups.

22 pages, 14 tables

References in corpus (6)

• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Classification of 6-dimensional real Drinfeld doubles
• Poisson-Lie T-dual sigma models on supermanifolds
• Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups
• Classification of two and three dimensional Lie super-bialgebras
• Classification of four and six dimensional Drinfel'd superdoubles

Cited by in corpus (7)

• Poisson-Lie T-dual sigma models on supermanifolds
• The gl(1|1) Lie superbialgebras
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model