Algebraic spin structures

Abstract

A different type of spin structure based on the algebraic notion of a spinor space and not on the double covering of the special orthogonal group is considered. The existence of these structures is less restrictive than that of normal spin structures and is examined in terms of obstruction classes. The existence of minimal left ideal bundles and primitive idempotent sections is also studied. In this context Roger Penrose’s notion of a flag is generalized to give a geometric characterization of minimal left ideals of a real Clifford algebra C _{p, q} with 0 ≤ q < p ≤ 3.