Spinor modules of Clifford algebras in classes \(N_{2k-1}\) and \(\Omega _{2k-1}\) are determined by irreducible nonlinear characters of corresponding Salingaros vee groups
The goal of this paper is to prove that for any \(k \in \{1,2,3,4\}\) and any Salingaros vee group \(G_{p,q}\) in classes \(N_{2k-1}\) or \(\Omega_{2k-1}\), each character of \(G_{p,q}\) can be realized over \(\mathbb{R}\). As a result, every nonlinear character of \(G_{p,q}\) uniquely determines a spinor module of \(C\ell_{p,q}\) which is faithful for classes \(N_{2k-1}\) and unfaithful for classes \(\Omega_{2k-1}\). This generalizes a known fact on the isomorphic Clifford algebras \(C\ell_{2,0}\) and \(C\ell_{1,1}\), whose Salingaros vee groups belong to the class \(N_1\).
scientific article; zbMATH DE number 6918635
scientific article