When Is a Bogolyubov Automorphism Inner?

TL;DR

This paper characterizes when Bogolyubov automorphisms of Clifford algebras, induced by orthogonal transformations, are inner, providing necessary and sufficient conditions in the context of infinite-dimensional vector spaces.

Contribution

It establishes precise criteria for when Bogolyubov automorphisms of Clifford algebras are inner, extending understanding of automorphism structures in infinite-dimensional settings.

Findings

Derived necessary and sufficient conditions for inner Bogolyubov automorphisms.

Connected automorphism properties to the structure of orthogonal transformations.

Enhanced the theoretical framework of Clifford algebra automorphisms.

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.