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Abstract
In this paper we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the FreundRubin backgrounds, and propose a geometric construction extending the wellknown construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric FreundRubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS(4) x S7 and find that it is isomorphic to osp(1 vertical bar 32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS(4) x S7 and we test this proposal by computing the maximal superalgebra of the M2brane in its two maximally supersymmetric limits, finding agreement.
Original language  English 

Article number  035016 
Number of pages  17 
Journal  Classical and quantum gravity 
Volume  26 
Issue number  3 
DOIs  
Publication status  Published  Feb 2009 
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 1 Finished

The classification and geometry of supersymmetric supergravity solutions
HackettJones, E.
1/11/04 → 31/10/07
Project: Research