Poisson–Lie identities and dualities of Bianchi cosmologies

Abstract

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