On modular spaces of semisimple Drinfeld doubles

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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15 pages; introduction enlarged, added references

Scientific paper

10.1088/1126-6708/2002/09/018

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.

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