Related papers: Jordan C*-Algebras and Supergravity
Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian.…
We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities,…
As open N=2 or 4 strings describe self-dual N=4 super Yang-Mills in 2+2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) N=8 supergravity. These theories are conveniently formulated in a chiral…
A representation of the exceptional Lie algebras is presented. It reflects a simple unifying view and it is realized in terms of Zorn-type matrices. The role of the underlying Jordan pair and Jordan algebra content is crucial in the…
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local…
We derive a theory of quantum gravity containing an AdS$_3$ isometry/qubit duality. The theory is based on a superalgebra generalization of the enveloping algebra of the homogeneous AdS$_3$ spacetime isometry group and is isomorphic to the…
We present a geometrical description of N=8 supergravity, using central charge superspace. The essential properties of the multiplet, like self-duality properties of the vectors or the non-linear sigma model structure of the scalars, are…
We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality…
We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known…
In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…
We present a periodic infinite chain of finite generalisations of the exceptional structures, including the exceptional Lie algebra $\mathbf{e_8}$, the exceptional Jordan algebra (and pair) and the octonions. We will also argue on the…
Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3 are considered. The close connections of these algebras with Lie algebras graded over the nonreduced root system BC1, with J-ternary algebras and with…
We consider the dimensional reduction to D = 3 of four maximal-rank supergravities which preserve minimal supersymmetry in D = 11, 7, 5 and 4. Such "curious" theories were investigated some time ago, and the four-dimensional one corresponds…
For a C*-algebra A, G. Pedersen defined the concept of universal measurability for self-adjoint elements of A**, the universal enveloping algebra of A. Although he was unable to show that U, the set of universally measurable elements, is a…
While most theorists are tied to the mast of four dimensions, some have found it irresistible to speculate about eleven dimensions, the domain of M-theory. We outline a program which starts from the light-cone description of supergravity,…
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,…
The Jordan algebra of the symmetric matrices of order two over a field $K$ has two natural gradings by $\mathbb{Z}_2$, the cyclic group of order 2. We describe the graded polynomial identities for these two gradings when the base field is…
We developed a new proper method for classifying $n$-dimensional derived Jordan algebras, and apply it to the classification of $3$-dimensional derived Jordan algebras. As a byproduct, we have the algebraic classification of $3$-dimensional…
We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We…
The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a…