Poisson-Lie T-plurality on decompositions of Drinfeld doubles from Manin triples yields curved backgrounds with torsion solving generalized supergravity equations, many interpretable as homogeneous Yang-Baxter deformations.
Classification of 6-dimensional real Drinfeld doubles
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abstract
Starting from the classification of real Manin triples done in a previous paper we look for those that are isomorphic as 6-dimensional Lie algebras with the ad-invariant form used for construction of the Manin triples. We use several invariants of the Lie algebras to distinguish the non-isomorphic structures and give explicit form of maps between Manin triples that are decompositions of isomorphic Drinfeld doubles. The result is a complete list of 6-dimensional real Drinfeld doubles. It consists of 22 classes of non-isomorphic Drinfeld doubles.
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Eight-dimensional Manin triples, Yang-Baxter deformations and solutions of Supergravity Equations
Poisson-Lie T-plurality on decompositions of Drinfeld doubles from Manin triples yields curved backgrounds with torsion solving generalized supergravity equations, many interpretable as homogeneous Yang-Baxter deformations.