On modular spaces of semisimple Drinfeld doubles

Abstract

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different from the known one for Abelian Drinfeld double, since some of these Drinfeld doubles allow decomposition into several non-isomorphic Manin triples and their modular spaces are therefore written as unions of homogeneous spaces of different dimension. Implications for Poisson-Lie T-duality and especially Poisson-Lie T-plurality are mentioned.

15 pages; introduction enlarged, added references

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Cited by in corpus (6)

• Poisson-Lie T-plurality
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models
• Quantization of Drinfel'd doubles
• The Drinfeld double gl(n) \oplus t_n
• Comments on Dualities on Group Manifolds and Supersymmetry