The primitive idempotents of the clifford algebras and the amorphic spinor fibre bundles

Abstract

We intend to clarify the “primitive idempotent” method of defining spinor bundles as fields of minimal ideas in some Clifford algebra bundles. The fundamental notion of “geometric Cliffordian spinoriality groups” is introduced, a notion similar to that of “groupes de spinorialité” defined previously [1d] by the author, but not equivalent. Existence conditions depend on the choice of the standard left ideal and provide a “chaotic character” for physics. Existence conditions of primitive idempotent fields imply drastic conditions. We give several examples. The primitive idempotent method brings algebraic tools, but raises a lot of geometric obstacles and cannot replace, improve or generalize the “ r-isotropic” approach [1].