Classification of Nottingham algebras

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.

💡 Research Summary

The paper completes the classification of Nottingham algebras, a distinguished family of infinite‑dimensional, positively graded thin Lie algebras defined over a field of odd prime characteristic p > 3. A thin Lie algebra L is generated by two degree‑1 elements x and y and satisfies the covering property: for every non‑zero z∈L_i, the bracket