When is a Bogolyubov automorphism inner?

Abstract

Let \(V\) be an infinite-dimensional vector space over a field of characteristic not equal to \(2\). Given a nondegenerate quadratic form \(f\) on \(V,\) we consider the Clifford algebra \(\mathrm{Cl}(V,f)\). Any orthogonal linear transformation of \(V\) extends to a Bogolyubov automorphism of \(\mathrm{Cl}(V,f)\). We obtain necessary and sufficient conditions for a Bogolyubov automorphism to be inner.