On the classification of Clifford algebras as quadratic spaces in the case where the dimension is infinite and the base field has characteristic 2

Abstract

We consider the cliffordalgebra of a quadratic space (E, Q) equipped with a quadratic form that extends Q. In the case where the characteristic of the base field k is 2, [$\dot k:\dot k$ ²] is finite and the dimension of E is infinite but less than ℵ_ω0 we characterize the extended form by a finite number of invariants. This turns out by using linear topologies on E assigned with the quadratic form and an application of lattice theory in the theory of quadratic forms.