Eleven-dimensional symmetric supergravity backgrounds, their geometric   superalgebras, and a common reduction
  We present two different families of eleven-dimensional manifolds that admit non-restricted extensions of the isometry algebras to geometric superalgebras. Both families admit points for which the superalgebra extends to a super Lie algebra; on the one hand, a family of $N=1$, $\nu={}^3\!/\!_4$ supergravity backgrounds and, on the other hand, a family of $N=1$, $\nu=1$ supergravity background. Furthermore, both families admit a point that can be identified with an $N=4$, $\nu={}^1\!/\!_2$ six-dimensional supergravity background. 
Frank Klinker
hep-th math.DG