Deformations of M-theory Killing superalgebras

We classify the Lie superalgebra deformations of the Killing superalgebras of some M-theory backgrounds. We show that the Killing superalgebras of the Minkowski, Freund--Rubin and M5-brane backgrounds are rigid, whereas the ones for the M-wave, the Kaluza--Klein monopole and the M2-brane admit deformations, which we give explicitly.Comment: 20 pages (v3: a number of signs and a couple of factors have changed without affecting the result. v4: yet more sign changes, but results remain unchanged. v5: this is becoming absurd... but the signs ought to be correct now! v6: no more sign changes, but section 5.2 on the MKK monopole has been partially rewritten and some relevant references have been added.

Metric Lie n-algebras and double extensions

We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from the simple and one-dimensional ones by iterating the operations of orthogonal direct sum and double extension.Comment: 10 page

The homogeneity theorem for supergravity backgrounds II: the six-dimensional theories

We prove that supersymmetry backgrounds of (1,0) and (2,0) six-dimensional supergravity theories preserving more than one half of the supersymmetry are locally homogeneous. As a byproduct we also establish that the Killing spinors of such a background generate a Lie superalgebra.Comment: 16 page

Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities

We classify (up to local isometry) the maximally supersymmetric solutions of the eleven- and ten-dimensional supergravity theories. We find that the AdS solutions, the Hpp-waves and the flat space solutions exhaust them.Comment: 24 page

Deformations of 3-algebras

We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern--Simons theories with matter.Comment: 29 pages (V2: one error corrected: section 5.2 considerably shorter now