Avitabile, Marina and Mattarei, Sandro (2021) Diamond distances in Nottingham algebras. Journal of Algebra and Its Applications . ISSN 02194988
Full content URL: https://doi.org/10.1142/S0219498823500329
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
Nottingham algebras are a class of justinfinitedimensional, modular, Ngraded 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. Many examples of Nottingham algebras are known, in which each diamond past the first can be assigned a type, either belonging to the underlying field or equal to infinity.
A prospective classification of Nottingham algebras requires describing all possible diamond patterns. In this paper we establish some crucial contributions towards that goal. One is showing that all diamonds, past the first,
of an arbitrary Nottingham algebra L can be assigned a type, in such a way that the degrees and types of the diamonds completely describe L. At the same time we prove that the difference in degrees of any two consecutive diamonds in any Nottingham algebra equals q1. As a sideproduct of our investigation, we classify the Nottingham algebras where all diamonds have type infinity.
Keywords:  modular Lie algebra, graded Lie algebra, thin Lie algebra 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
ID Code:  47134 
Deposited On:  08 Nov 2021 11:20 
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