The Jordan Pair content of the magic square and the geometry of the scalars in N=2 supergravity |
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Authors: | P. Truini G. Olivieri L. C. Biedenharn |
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Affiliation: | (1) Dipartimento di fisica, Universitá di Genova, 16146 Genoa, Italy;(2) Department of Physics, Duke University, 27706 Durham, NC, USA |
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Abstract: | ![]() The close connection between Jordan and Lie algebras makes these Jordan structures of interest to physicists. The Freudenthal-Tits Magic Square, which exemplifies this connection, has recently entered into constructing supergravity. We show how Jordan pairs-which are, from several points of view, a most natural Jordan structure-are imbedded in the Magic Square. We compare our approach with that of Gürsey and show show the Hermitian symmetric spaces parametrized by the scalars of N=2, d=4 supergravity theories are related either to Jordan pairs or to geometries of projective dimension two, whose elements belong to a Jordan pair. |
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