A construction of matrix representation of Clifford algebras (Q497168)

The main result is a recursive construction of a subalgebra \(S_{2^n}({\mathbb R})\) of the full matrix algebra \(M_{2^n}({\mathbb R})\) with the following property: \(S_{2^n}({\mathbb R})\) is isomorphic to the Clifford algebra of the \(n\)-dimensional pseudo-Euclidean vector space with signature \((p,q)\), where either \(p=q=n/2\) (for \(n\) even) or \(p-1=q=[n/2]\) (for \(n\) odd). Furthermore, the problem of invertibility of certain elements of the algebra \(S_{2^n}({\mathbb R})\) is addressed.