# Paper accepted by Journal of Lie Theory

A paper by Marina Avitabile and Sandro Mattarei, *The earliest diamond of finite type in Nottingham algebras,* has been accepted for publication in *Journal of Lie Theory*. (See https://arxiv.org/abs/2106.14796 for a preprint version. The photograph is a portrait of Sophus Lie, 1896.)

*Abstract*: We prove several structural results on *Nottingham algebras*, a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. Homogeneous components of a Nottingham algebra have dimension one or two, and in the latter case they are called *diamonds*. The first diamond occurs in degree 1, and the second occurs in degree *q*, a power of the characteristic. Each diamond past the second is assigned a *type*, which either belongs to the underlying field or is ∞. Nottingham algebras with a variety of diamond patterns are known. In particular, some have diamonds of both finite and infinite type. We prove that each of those known examples is uniquely determined by a certain finite-dimensional quotient. Finally, we determine how many diamonds of type ∞ may precede the earliest diamond of finite type in an arbitrary Nottingham algebra.

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