Abstract
We present two different families of eleven-dimensional manifolds that admit non-restricted extensions of their isometry algebras to geometric su- peralgebras. Both families admit points for which the superalgebra extends to a super Lie algebra; on the one hand, a family of N = 1, = 3=4 supergravity backgrounds and, on the other hand, anN = 1, = 1 supergravity background. Furthermore, both families admit a point that can be identified with an N = 4, = 1=2 six-dimensional supergravity background.
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