Since W ′ is isotropic, multiplication of elements of W ′ inside Cℓ(V, g) is skew. Hence vectors in W ′ anti-commute, and Cℓ(W ′, g | W ′) = Cℓ(W ′, 0) is just the exterior algebra Λ W ′. Consequently, the k -fold product of W ′ with itself, W ′, is one-dimensional. Let ω be a generator of W ′. In terms of a basis w ′ 1,..., w ′ k of in W ′, one possibility is to set ω ω = w 1 ′ w 2 ′ ⋯ ⋯ w k ′ .