# Poisson-Lie identities and dualities of Bianchi cosmologies

## TL;DR

This paper explores Poisson-Lie T-plurality transformations in Bianchi cosmologies, identifying their structure and generating new solutions to Generalized Supergravity Equations through specific dualities and automorphisms.

## Contribution

It provides a detailed decomposition of Poisson-Lie identities and dualities for Bianchi cosmologies, enabling the construction of new supergravity backgrounds.

## Key findings

- Identified general forms of Poisson-Lie identities and dualities for Bianchi cosmologies.
- Decomposed transformations into automorphisms, B-shifts, β-shifts, and dualities.
- Generated new supergravity solutions supported by dilatons.

## 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 $\mathfrak{b}\bowtie \mathfrak{a}$ 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.