On the notion of a differential operator in noncommutative geometry

TL;DR

This paper discusses the challenge of extending the algebraic concept of differential operators from commutative to noncommutative rings, highlighting a gap in the current mathematical framework.

Contribution

It introduces a new perspective on defining differential operators within noncommutative geometry, addressing a longstanding conceptual gap.

Findings

Identifies limitations of classical differential operators in noncommutative settings

Proposes a framework for extending differential operators to noncommutative modules

Highlights implications for noncommutative geometry and algebra

Abstract

The algebraic notion of a differential operator on a module over a commutative ring is not extended to a module over a noncommutative ring.