Diffeological Clifford algebras and pseudo-bundles of Clifford modules

TL;DR

This paper develops the theory of Clifford algebras and modules within the framework of diffeology, introducing pseudo-bundles and exploring their properties through gluing techniques.

Contribution

It introduces the concept of diffeological Clifford algebras and modules, and constructs pseudo-bundles using diffeological gluing, expanding the framework of diffeological algebra.

Findings

Defined diffeological Clifford algebras and modules

Constructed pseudo-bundles via diffeological gluing

Provided expository insights into diffeological algebras

Abstract

We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that of a diffeological module (also an expected counterpart of the usual notion). After considering the natural diffeology of the Clifford algebra, and its expected properties, we turn to our main interest, which is constructing pseudo-bundles of diffeological Clifford algebras and those of diffeological Clifford modules, by means of the procedure called diffeological gluing. The paper has a significant expository portion, regarding mostly diffeological algebras and diffeological vector pseudo-bundles.