Classification of Nottingham algebras

TL;DR

This paper completes the classification of Nottingham algebras, a special class of infinite-dimensional graded Lie algebras, by establishing existence and uniqueness results for all such algebras.

Contribution

It provides a complete classification of Nottingham algebras, resolving previous open questions about their structure and uniqueness.

Findings

Proves existence of all Nottingham algebras

Establishes uniqueness up to isomorphism

Completes the classification program for Nottingham algebras

Abstract

The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensional, positively graded thin algebras. This paper completes the classification of Nottingham algebras initiated in earlier papers, proving both existence and uniqueness results that determine all such algebras up to isomorphism.