“…Interestingly, a broad class of FGT gauge algebras is provided by the Lie algebras "of type e7" which occur as conformal symmetries of Euclidean Jordan algebras of rank 3, and as U-duality algebras of the corresponding (super)gravity theories in D = 4. …”
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“…The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. …”
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“…We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. …”
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“…By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity theories. …”
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“…We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. …”
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“…Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.…”
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“…Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N=0 and N=1 AdS_4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. …”
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“…In order to elucidate the connections of this formalism to four-dimensional Maxwell-Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric N = 2 stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrepr. of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.…”
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“…The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U-)duality group G4. We start with an algebraic approach based on classical invariant theory, using Schur polynomials and the Cauchy formula. …”
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