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 $\mathfrak{b}\bowtie \mathfrak{a}$ containing Bianchi algebras $\mathfrak{b}$ 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, $\beta$-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.