The Graf product: a Clifford structure framework on the exterior bundle

TL;DR

This paper introduces and revisits the Graf product, a geometric product on differential forms, providing a comprehensive Clifford algebra framework that incorporates coframes, volume elements, and the Hodge operator.

Contribution

It presents a new framework for the Graf product that naturally includes coframes and other geometric structures within the Clifford algebra setting.

Findings

Defines the Graf product within a unified Clifford structure

Shows how the framework encompasses coframes and volume elements

Provides insights into the algebraic properties of differential forms

Abstract

The geometric product, defined by Graf on the space of differential forms, endows the sections of the exterior bundle by a structure that is necessary to construct a Clifford algebra. The Graf product is introduced and revisited with a suitable underlying framework that naturally encompasses a coframe in the cotangent bundle, besides the volume element centrality, the Hodge operator and the so called truncated subalgebra as well.