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Poisson-Lie T-duality and plurality are important solution generatingtechniques in string theory and (generalized) supergravity. Sinceduality/plurality does not preserve conformal invariance, the usual betafunction equations are replaced by Generalized Supergravity Equationscontaining vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-pluralityon Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ aswell as transformation rule for dilaton, and show that plural backgroundstogether with this dilaton and $\mathcal{J}$ satisfy the GeneralizedSupergravity Equations. The procedure is valid also for non-local dilaton andnon-constant $\mathcal{J}$. We also show that $Div\,\Theta$ of thenon-commutative structure $\Theta$ used for non-Abelian T-duality or integrabledeformations does not give correct $\mathcal{J}$ for Poisson-Lie T-plurality.

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations