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Poisson-Lie plurals of Bianchi cosmologies and generalized supergravity equations. (English) Zbl 1436.83097

Summary: Poisson-Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector \(\mathcal{J}\). In this paper we apply Poisson-Lie T-plurality on Bianchi cosmologies. We present a formula for the vector \(\mathcal{J}\) as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and \(\mathcal{J}\) satisfy the Generalized Supergravity Equations. The procedure is valid also for non-local dilaton and non-constant \(\mathcal{J}\). We also show that \(Div \Theta\) of the non-commutative structure \(\Theta\) used for non-abelian T-duality or integrable deformations does not give correct \(\mathcal{J}\) for Poisson-Lie T-plurality.

MSC:

83E50 Supergravity
83F05 Relativistic cosmology
81R12 Groups and algebras in quantum theory and relations with integrable systems
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