On Clifford Algebras of Infinite Dimensional Vector Spaces

TL;DR

This paper investigates the structure of Clifford algebras over infinite-dimensional vector spaces, focusing on derivations and automorphisms, including non-continuous automorphisms in the algebraic setting.

Contribution

It characterizes derivations of Clifford algebras for countably infinite-dimensional spaces and constructs a non-continuous algebraic automorphism, advancing understanding of their algebraic properties.

Findings

Derivations of Clifford algebras are described for countable dimensions.

An algebraic automorphism that is not continuous is constructed.

Provides insights into the algebraic automorphism structure of infinite-dimensional Clifford algebras.

Abstract

We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of the Clifford algebra of a positive definite quadratic form that is not continuous.