Embedding rational division algebras

Embedding problems of division algebras

A finite group G is called admissible over a given field if there exists a central division algebra that contains a G-Galois field extension as a maximal subfield. We give a definition of embedding problems of division algebras that extends both the notion of embedding problems of fields as in classical Galois theory, and the question which finite groups are admissible over a field. In a recent...

Triangulaizability of Algebras Over Division Rings

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 ...

Left-distributive Embedding Algebras

We consider algebras with one binary operation and one generator, satisfying the left distributive law a (b c) = (a b) (a c); such algebras have been shown to have surprising connections with set-theoretic large cardinals and with braid groups. One can construct a sequence of nite left-distributive algebras An, and then take a limit to get an in nite left-distributive algebra A1 on one generato...

Finite Left{distributive Algebras and Embedding Algebras

We consider algebras with one binary operation and one generator (monogenic) and satisfying the left distributive law a (b c) = (a b) (a c). One can de ne a sequence of nite left-distributive algebras An, and then take a limit to get an in nite monogenic left-distributive algebra A1. Results of Laver and Steel assuming a strong large cardinal axiom imply that A1 is free; it is open whether the ...