  We show how supersymmetry conditions for flux compactifications of
supergravity and string theory can be described in terms of a flat subalgebra
of the Kahler-Atiyah algebra of the compactification space, a description which
has wide-ranging applications. As a motivating example, we consider the most
general M-theory compactifications on eight-manifolds down to AdS3 spaces which
preserve N=2 supersymmetry in 3 dimensions. We also give a brief sketch of the
lift of such equations to the cone over the compactification space and of the
geometric algebra approach to `constrained generalized Killing pinors', which
forms the technical and conceptual core of our investigation.
