Selectivity in division algebras

Triangulaizability of Algebras Over Division Rings

Selectivity in Quaternion Algebras

Let A be a quaternion algebra over a number field K and assume that A satisfies the Eichler condition; that is, there exists an archimedean prime of K which does not ramify in A. Let Ω be a commutative, quadratic OK-order and let R ⊂ A be an order. We determine the isomorphism classes in the genus of R which admit an embedding of Ω. In particular, we show that the proportion of the genus of R a...

Correspondences between Valued Division Algebras and Graded Division Algebras

If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map ...

On Nonassociative Division Algebras^)

Division Algebras and Supersymmetry

Supersymmetry is deeply related to division algebras. For example, nonabelian Yang–Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green–Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain trilinear expression involving a spinor field. The reason for this...