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Gal'tsov, G\\'erard Cl\\'ement","submitted_at":"2013-01-14T16:06:25Z","abstract_excerpt":"Toroidal reduction of minimal six-dimensional supergravity, minimal five-dimensional supergravity and four-dimensional Einstein-Maxwell gravity to three dimensions gives rise to a sequence of cosets $O(4,3)/(O(4)\\times O(3))\\supset G_{2(2)}/(SU(2)\\times SU(2))\\supset SU(2,1)/S(U(2)\\times U(1))$ which are invariant subspaces of each other. The known matrix representations of these cosets, however, are not suitable to realize these embeddings which could be useful for solution generation. 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