Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Banach Center Publications / All volumes

Abstract

Let V be a ℂ-space, $σ ∈ End(V^{⊗2})$ be a pre-braid operator and let $F ∈ lin(V^{⊗2},ℂ).$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $Cl(V,σ,0) ≡ V^{∧}(σ)$. If $σ ≠ σ^{-1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation is faithful and irreducible.