 Pure spinors were introduced into the realm of theoretical physics, and elevated in their importance in the study of spin geometry more generally, by Roger Penrose in the 1960s, where they became among the basic objects of study in twistor theory.Consider a complex vector space C2"n" with even complex dimension 2"n" and a quadratic form "Q", which maps a vector "v" to complex number "Q"("v").The Clifford algebra "C"ℓ2n(C) is the ring generated by products of vectors in C2"n" subject to the relation

Spinors are modules of the Clifford algebra, and so in particular there is an action of C2"n" on the space of spinors.