@article{eed3ccb4561d4ec39ee85397cd3361a3, title = "Spencer Cohomology and 11-Dimensional Supergravity", abstract = "We recover the classification of the maximally supersymmetric bosonic backgrounds of 11-dimensional supergravity by Lie algebraic means. We classify all filtered deformations of the ZZ -graded subalgebras h=h−2⊕h−1⊕h0h=h−2⊕h−1⊕h0 of the Poincar{\'e} superalgebra g=g−2⊕g−1⊕g0=V⊕S⊕so(V)g=g−2⊕g−1⊕g0=V⊕S⊕so(V) which differ only in zero degree, that is h0⊂g0h0⊂g0 and hj=gjhj=gj for j<0j<0 . Aside from the Poincar{\'e} superalgebra itself and its ZZ -graded subalgebras, there are only three other Lie superalgebras, which are the symmetry superalgebras of the non-flat maximally supersymmetric backgrounds. In passing we identify the gravitino variation with (a component of) a Spencer cocycle.", author = "Jose Figueroa-O'Farrill and Andrea Santi", year = "2017", month = jan, doi = "10.1007/s00220-016-2700-1", language = "English", volume = "349", pages = "627--660", journal = "Communications in Mathematical Physics", issn = "0010-3616", publisher = "Springer New York", number = "2", }