Jordan Algebras Of Degree Research Articles

Orbits and attractors for [formula omitted] Maxwell–Einstein supergravity theories in five dimensions

BPS and non-BPS orbits for extremal black-holes in N=2 Maxwell–Einstein supergravity theories (MESGT) in five dimensions were classified long ago by the present authors for the case of symmetric scalar manifolds. Motivated by these results and some recent work on non-supersymmetric attractors we show that attractor equations in N=2 MESGTs in d=5 do indeed possess the distinct families of solutions with finite Bekenstein–Hawking entropy. The new non-BPS solutions have non-vanishing central charge and matter charge which is invariant under the maximal compact subgroup K˜ of the stabilizer H˜ of the non-BPS orbit. Our analysis covers all symmetric space theories G/H such that G is a symmetry of the action. These theories are in one-to-one correspondence with (Euclidean) Jordan algebras of degree three. In the particular case of N=2 MESGT with scalar manifold SU∗(6)/USp(6) a duality of the two solutions with regard to N=2 and N=6 supergravity is also considered.

Representations of Rank 3 Algebras

The class of rank 3 algebras includes the Jordan algebra of a symmetric bilinear form, the trace zero elements of a Jordan algebra of degree 3, pseudo-composition algebras, certain algebras that arise in the study of Riccati differential equations, as well as many other algebras. We investigate the representations of rank 3 algebras and show under some conditions on the eigenspaces of the left multiplication operator determined by an idempotent element that the finite-dimensional irreducible representations are all one-dimensional.

Special Identity for Novikov–Jordan Algebras

ABSTRACT A commutative algebra with the identity (a * b) * (c * d) − (a * d) * (c * b) = (a, b, c) * d − (a, d, c) * b is called Novikov–Jordan. Example: K[x] under multiplication a * b = ∂(ab) is Novikov–Jordan. A special identity for Novikov–Jordan algebras of degree 5 is constructed. Free Novikov–Jordan algebras with q generators are exceptional for any q ≥ 1. #Communicated by I. Shestakov.

Jordan algebras of degree 3 and the Tits process

Jordan algebras of degree 3 and the Tits process

Convex cones, Jordan algebras and the geometry of d=9 Maxwell-Einstein supergravity

The authors show that the Riemannian manifold characterising the scalar field interactions of d=9 Maxwell-Einstein (ME) supergravity is the convex cone associated with a Jordan algebra of degree 2. The result is similar to that of a class of d=5, N=2, ME supergravity theories associated with Jordan algebras of degree 3. They also construct the unique irreducible d=9 Yang-Mills supergravity which has non-compact gauge group Sl(2; R).

Minimal identities for jordan algebras of degree 2

In this note we give a basis for the space of multilinear Jordan polynomials of degree 5 which are identities for all Jordan algebras of degree 2 that Is for all algebras J(Q,1) obtained from a quadratic form Q These basic identities are all derived by linearizing the identity for S 3 the standard polynomial of degree 3.

Cubic Subfields of Exceptional Simple Jordan Algebras

Let $E/k$ be a cubic field extension and $J$ a simple exceptional Jordan algebra of degree 3 over $k$. Then $E$ is a reducing field of $J$ if and only if $E$ is isomorphic to a (maximal) subfield of some isotope of $J$. If $k$ has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over $k$ contains a cyclic cubic subfield.

Cubic subfields of exceptional simple Jordan algebras

Let E / k E/k be a cubic field extension and J J a simple exceptional Jordan algebra of degree 3 over k k . Then E E is a reducing field of J J if and only if E E is isomorphic to a (maximal) subfield of some isotope of J J . If k k has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over k k contains a cyclic cubic subfield.

Generalized simple noncommutative Jordan algebras of degree two

Generalized simple noncommutative Jordan algebras of degree two

A Norm on Separable Noncommutative Jordan Algebras of Degree 2

A Norm on Separable Noncommutative Jordan Algebras of Degree 2

Jordan algebras of degree 1

Jordan algebras of degree 1

V.—On Certain Classes of Linear Algebras of Genus One

SynopsisA result proved elsewhere concerning the structure of linear algebras of genus one is used (i) to classify Jordan algebras of genus one, and (ii) to obtain necessary and sufficient conditions for an algebra of genus one to be simple. The class of simple Jordan algebras of genus one and dimension not less than 4 over an algebraically closed field is shown to coincide with the class of simple Jordan algebras of degree two.