Hodge-theoretic obstruction to the existence of quaternion algebras

Hodge-theoretic Obstruction to Existence of Quaternion Algebras

The subject of this paper is the Brauer group of a nonsingular complex projective variety. More specifically, we study the question of whether a 2-torsion element of the cohomological Brauer group is representable by a quaternion algebra over the generic point. Using intersection theory – on schemes and on algebraic stacks – we are able to describe an obstruction to such a representation, and t...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras

New Values for the Level and Sublevel of Composition Algebras

Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann’s proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.

CM points and quaternion algebras

2 CM points on quaternion algebras 4 2.1 CM points, special points and reduction maps . . . . . . . . . 4 2.1.1 Quaternion algebras. . . . . . . . . . . . . . . . . . . . 4 2.1.2 Algebraic groups. . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Adelic groups. . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.4 Main objects. . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.5 Galois action...