Classification of four and six dimensional Drinfel'd superdoubles

Abstract

Using adjoint representation we firstly classify two and three dimensional Lie super-bialgebras obtain from decomposable Lie superalgebras. In this way we complete the classification obtained by Eghbali et al., [J. Math. Phys. 51, 073503 (2010); e-print arXiv:0901.4471 [math-ph]]. Then we classify all four and six dimensional Drinfel'd superdoubles.

28 pages, 7 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
• Manin supertriples and Drinfel'd superdoubles in low dimensions

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• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ and deformation of related integrable Hamiltonian systems
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality
• 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