| Summary: | Abstract We present all the symmetry superalgebras g $$ \mathfrak{g} $$ of all warped AdS k × w M d − k , k > 2, flux backgrounds in d = 10, 11 dimensions preserving any number of supersymmetries. First we give the conditions for g to decompose into a direct sum of the isometry algebra of AdS k and that of the internal space M d − k . Assuming this decomposition, we identify all symmetry superalgebras of AdS3 backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and d = 11 theories the AdS3 symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS3 backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdS k , k > 3, backgrounds and prove that they are all classical.
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