
Journal of Lie Theory 32 (2022), No. 3, 771796 Copyright Heldermann Verlag 2022 The Earliest Diamond of Finite Type in Nottingham Algebras Marina Avitabile Università degli Studi di MilanoBicocca, Milano, Italy marina.avitabile@unimib.it Sandro Mattarei Charlotte Scott Centre for Algebra, University of Lincoln, United Kingdom smattarei@lincoln.ac.uk We prove several structural results on Nottingham algebras, a class of infinitedimensional, 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 finitedimensional quotient. Finally, we determine how many diamonds of type ∞ may precede the earliest diamond of finite type in an arbitrary Nottingham algebra. Keywords: Modular Lie algebra, graded Lie algebra, thin Lie algebra. MSC: 17B50; 17B70, 17B65. [ Fulltextpdf (176 KB)] for subscribers only. 