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We perform a complete classification of the flux-induced 12d algebrascompatible with the set of N=1 type II orientifold models that are T-dualityinvariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropicorbifold. The classification is performed in a type IIB frame, where only H_3and Q fluxes are present. We then study no-go theorems, formulated in a typeIIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By derivinga dictionary between the sources of potential energy for the three moduli (S, Tand U) in types IIA and IIB, we are able to combine algebra results and no-gotheorems. The outcome is a systematic procedure for identifyingphenomenologically viable models where Mkw/dS vacua may exist. We present acomplete table of the allowed algebras and the viability of their resultingscalar potential, and we point at the models which stand any chance ofproducing a fully stable vacuum.

Flux moduli stabilisation, Supergravity algebras and no-go theorems