Clifford groups for arbitrary quadratic forms

Abstract

As it is, this article will explain that there are sensible ways to define a Clifford group even for a degenerate quadratic form; but I am not especially interested about degenerate quadratic forms; I am interested in defining Clifford groups in algebras which look like classical Clifford algebras, but are not so easy to study; and I have come to the conclusion that many important ideas already appear when one is working with degenerate quadratic forms. I propose to define the Clifford group as the group of invertible elements in a monoid (or semi-group), which I shall call the Clifford monoid, and which is in the classical cases the closure of the Clifford group for any sensible topology (for instance a topology of normed vector space, or the Zariski topology of algebraic geometry).