Irreducible Clifford modules. (Q1411736)

Let \(C\ell_n\) be the complex Clifford algebra on \(\mathbb{C}^n\), and let \(\Delta_{2n}\) be the irreducible \(C\ell_{2n}\)-module. The author uses the bimodule isomorphism \(C\ell_{2n}\cong \Delta\times \Delta\) to derive matrix representations of \(C\ell_{2n}\) and hence to exhibit a list of generators of the irreducible modules over \(C\ell_n\), for all \(n\). The algebra \(C\ell_s\) is examined in detail, and a relationship between Clifford algebras and the octonions is presented.