Poisson-Lie identities and dualities of Bianchi cosmologies

We investigate a special class of Poisson-Lie T-plurality transformations of Bianchi cosmologies invariant with respect to non-semisimple Bianchi groups. For six-dimensional semi-Abelian Manin triples b⋈a containing Bianchi algebras b we identify general forms of Poisson-Lie identities and dualities. We show that these can be decomposed into simple factors, namely automorphisms of Manin triples, B-shifts, β-shifts, and "full" or "factorized" dualities. Further, we study effects of these transformations and utilize the decompositions to obtain new backgrounds which, supported by corresponding dilatons, satisfy Generalized Supergravity Equations.