Fake Galois actions

We prove that for all non-abelian finite simple groups [Formula: see text], there exists a fake [Formula: see text]th Galois action on [Formula: see text] with respect to [Formula: see text], where [Formula: see text] is the universal covering group of [Formula: see text] and [Formula: see text] is any non-negative integer coprime to the order of [Formula: see text]. This is one of the two inductive conditions needed to prove an [Formula: see text]-modular analogue of the Glauberman–Isaacs correspondence.

SPONTANEOUS CP VIOLATION FROM A QUATERNIONIC KALUZA–KLEIN THEORY

Motivated by the isomorphism between the universal covering group of the six-dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant theory is postulated to exist in six space–time dimensions. Compactifying onto the space–time M4 ⊗ S2 a complex theory is retrieved on the four-dimensional Minkowski space with the essential quaternionic nature confined to S2. Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP-violating effect via spontaneous symmetry breaking.

ON CERTAIN TOPOLOGICAL ASPECTS OF THE FAMILY PROBLEM

Certain topological aspects of potential significance to the problem of family formation are investigated. Specifically, it is shown that the conventional vacuum state for gauge theories with non-trivial topology and fermions in the fundamental representation of the universal covering group of the gauge group, is not, in general, gauge invariant. The true gauge invariant vacuum, as well as the corresponding generating functionals are constructed. As a result, for the particular case of an SO(10) gauge symmetry over R3×S1 which is explicitly considered here, gauge and Lorentz invariance requires the existence of four-fermion generations.