On a Ring of Formal Pseudo-differential Operators

TL;DR

This paper explores non-commutative higher-dimensional local fields, exemplified by the ring of formal pseudo-differential operators, and extends the KP hierarchy to this context, advancing the understanding of integrable systems.

Contribution

It introduces a framework for non-commutative higher-dimensional local fields and extends the KP hierarchy to the space of pseudo-differential operators.

Findings

Extended KP hierarchy to the space P^n

Provided a new perspective on non-commutative local fields

Enhanced understanding of pseudo-differential operators in higher dimensions

Abstract

We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the KP hierarchy to the space $P^n$.