Related papers: Explicit Orbit Classification of Reducible Jordan …
We review various properties of the exceptional Euclidean Jordan algebra of degree three. Euclidean Jordan algebras of degree three and their corresponding Freudenthal triple systems were recently shown to be intimately related to extremal…
It is known that black hole charge vectors of N=8 and magic N=2 supergravity in four and five dimensions can be represented as elements of Jordan algebras of degree three over the octonions and split-octonions and their Freudenthal triple…
We study both the "large" and "small" U-duality charge orbits of extremal black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras…
Within the extremal black hole attractors arising in ungauged $\mathcal{N}\geqslant 2$-extended Maxwell Einstein supergravity theories in $3+1$ space-time dimensions, we provide an overview of the stratification of the electric-magnetic…
The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification,…
We determine and classify the electric-magnetic duality orbits of fluxes supporting asymptotically flat, extremal black branes in $D=4,5,6$ space-time dimensions in the so-called non-supersymmetric magic Maxwell-Einstein theories, which are…
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
We consider an integral version of the Freudenthal construction relating Jordan algebras and exceptional algebraic groups. We show how this construction is related to higher composition laws of M.Bhargava in number theory. We propose an…
The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x)…
In this paper, we will describe a combinatorial object to list the orbits in the ${\mathbb Z}$-graded Lie algebra, their Jordan bloc decomposition, their dimension, their dimension, the partial order and the equivariant local system (up to…
We derive the U-duality charge orbits, as well as the related moduli spaces, of "large" and "small" extremal black holes in non-maximal ungauged Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5 space-time dimensions.…
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various…
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity…
The aim of the present short note is to answer the open questions posted by Hern\'andez, Martin, and Rodrigues in {\rm \cite{p1,p2}}. The obtained results give the complete classification of irreducible components in the varieties of Jordan…
Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group $SU(3)$ and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to…
We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras,…
We extend the black hole/qudit correspondence by identifying five and six-dimensional 1/2-BPS black string and hole charge vectors in N=8 and N=2 magic supergravities with qubits and qutrits over composition algebras. In D=6, this is…
The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally…
The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple Lie superalgebras, specific to this characteristic, constructed in terms of orthogonal and symplectic triple…
We extend our previous study (arXiv:1203.5088) to the case of five-dimensional multi-charge black holes, thus showing that these configurations and their subtracted geometries also lie in a 3d duality orbit. In order to explore the 3d…