Realizing central division algebras

Triangulaizability of Algebras Over Division Rings

On realizing diagrams of ...–algebras

Given a diagram of ...–algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized ...–algebras. This extends a program begun by Dwyer, Kan, Stover, Blanc and Goe...

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 ...

Realizing Enveloping Algebras via Varieties of Modules

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(Λ) generated by indecomposable constructible sets in the varieties of modules for any finite dimensional Calgebra Λ. We obtain a geometric realization of the universal enveloping algebra R(Λ) of L(Λ). This generalizes the main result of Riedtmann in [19]. We also obtain Green’s theorem in [6] in a geome...

On Nonassociative Division Algebras^)