Square of an \(n\)-vector in an \(E_n\)
The paper presents elementary computations for real Clifford algebras (which can be easily generalized to other fields using appropriate notions). The author computes the square of \(A_n\) which is defined as the product (in the associated Clifford algebra) of an orthogonal basis of a real quadratic space of dimension \(n\), and shows that if \(A_r\) (\(r\leq n\)) denotes the product of the \(r\) first vectors of the given basis and \(A_{n-r}\) is the product of the remaining ones, then \(A_n\), \(A_r\) and \(A_{n-r}\) pairwise commute if and only if \((A_n)^2=(A_r)^2(A_{n-r})^2\).
scientific article; zbMATH DE number 1240575