{"arxiv_id":"0801.2763","incoming":{"papers":16,"sentences":28,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1001.1619","title":"The very-extended trombone","url":"/paper/1001.1619","section":"Conclusions","sentence":"The same applies to all supergravity theories with more than 16 supercharges [ref] .","intent_p":0.8,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":4,"quotes":[{"arxiv_id":"1110.4460","title":"Real forms of extended Kac-Moody symmetries and higher spin gauge theories","url":"/paper/1110.4460","section":"Introduction","sentence":"This results in very special real forms of Kac-Moody algebras that have not been discussed fully in the literature before (see, however, [ref] for the general theory and [ref] for some special cases and low level field content).","intent_p":0.86,"contests_p":null},{"arxiv_id":"0805.2573","title":"Extended Symmetries in Supergravity: the 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geometries","url":"/paper/hep-th/0606173","section":"Review of theories with eight supersymmetries","sentence":"Here $D_q+1$ is the dimension of the irreducible representation of the Clifford algebra in $q+1$ dimensions with positive signature, and takes the values $D_q+1=1 for q=-1,0$, $D_q+1=2 for q=1$, $D_q+1=4 for q=2$, $D_q+1=8 for q=3,4$, $D_q+1=16 for q=5,,6,7,8$ and $D_q+8=16D_q$ [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"hep-th/9112027","title":"Special geometry, cubic polynomials and homogeneous quaternionic spaces","url":"/paper/hep-th/9112027","section":"Review of theories with eight supersymmetries","sentence":"Here $D_q+1$ is the dimension of the irreducible representation of the Clifford algebra in $q+1$ dimensions with positive signature, and takes the values $D_q+1=1 for q=-1,0$, $D_q+1=2 for q=1$, $D_q+1=4 for q=2$, $D_q+1=8 for q=3,4$, $D_q+1=16 for q=5,,6,7,8$ and $D_q+8=16D_q$ [ref] 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reduction.","intent_p":0.85,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":20,"sentences":25,"quotes":[{"arxiv_id":"hep-th/0107209","title":"Coset Symmetries in Dimensionally Reduced Bosonic String Theory","url":"/paper/hep-th/0107209","section":"Introduction","sentence":"It was proposed that the bosonic string effective action generalised to $D$ dimensions is associated with the non-linear realisation of an algebra originally denoted by $K_27$ in the 26-dimensional case and which was later identified with $D_D-2^+++$ [ref] , and similarly gravity in $D$ dimensions is associated with $A_D-3^+++$ [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"hep-th/0104081","title":"E_11 and M Theory","url":"/paper/hep-th/0104081","section":"Introduction","sentence":"It was proposed that the bosonic string effective action generalised to $D$ dimensions is associated with the non-linear realisation of an algebra originally denoted by $K_27$ in the 26-dimensional case and which was later identified with $D_D-2^+++$ [ref] , and similarly gravity in $D$ dimensions is associated with $A_D-3^+++$ [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"hep-th/0107181","title":"Kac-Moody Symmetries of IIB Supergravity","url":"/paper/hep-th/0107181","section":"Introduction","sentence":"The original $E_11$ conjecture [ref] concerned the eleven dimensional supergravity theory, the ten dimensional IIA and IIB supergravity theories [ref] and their dimensional reductions.","intent_p":0.98,"contests_p":null},{"arxiv_id":"hep-th/0304206","title":"The Symmetry of M-Theories","url":"/paper/hep-th/0304206","section":"Relationship between Kac-Moody algebras and theories with eight supersymmetries","sentence":"Given a semi-simple finite dimensional algebra $G$ one constructs the very extended algebra $G^+++$ by adding to the Dynkin diagram of $G$ first the affine node and then the over extended node, which is connected to the affine node by a 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