Differential operators on non-commutative algebras

TL;DR

This paper extends the theory of differential operators from commutative to non-commutative algebras, providing a new construction that broadens understanding in algebraic analysis.

Contribution

It introduces a novel construction of differential operators on non-commutative algebras, generalizing existing commutative algebra results.

Findings

Constructs a framework for differential operators on non-commutative algebras

Establishes parallels with the commutative case

Provides foundational tools for further algebraic analysis

Abstract

There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily commutative algebras.