Smooth geometry of graded skew Clifford algebras
Andrés Rubiano
TL;DR
The paper addresses differential smoothness for graded (skew) Clifford algebras within Brzeziński–Sitarz noncommutative differential geometry, focusing on constructing integrable calculi of fixed dimension. It provides a practical sufficient criterion, involving independent data and compatible $\mu$-relations, to produce a differential calculus with a volume form and a dual integral calculus, proving differential smoothness for broad families including ordinary graded Clifford algebras. The results are demonstrated through multiple explicit examples, illustrating both applicability and the limits of the criterion. This work connects noncommutative geometry, Artin–Schelter regular algebras, and Clifford-type constructions, and suggests directions for extending the framework and relating it to other notions of regularity and noncommutative geometry.
Abstract
In this paper, we investigate the differential smoothness of graded skew Clifford algebras.