Abstract

We discuss algebraic spinors as elements of a minimal left ideal of the Clifford algebra and observe their factorization property as a ‘column times row’ in an arbitrary irreducible faithful matrix representation. This allows us to parametrize the set of primitive idempotents and the set of minimal left ideals, and find the dimensionality of the intersection of any minimal left with a minimal right ideal. We propose to generalize Cartan's concept of pure spinors to arbitrary linear spaceRp, q orCn.

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