
Journal of Lie Theory 19 (2009), No. 1, 185207 Copyright Heldermann Verlag 2009 Diamonds of Finite Type in Thin Lie Algebras Marina Avitabile Dip. di Matematica ed Applicazioni, Università di MilanoBicocca, Via Cozzi 53, 20125 Milano, Italy marina.avitabile@unimib.it Sandro Mattarei Dip. di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38050 Povo, Italy mattarei@science.unitn.it Borrowing some terminology from prop groups, thin Lie algebras are Ngraded Lie algebras, generated in degree one, of width two and obliquity zero. In particular, their homogeneous components have degree one or two, and they are termed diamonds in the latter case. In one of the two main subclasses of thin Lie algebras the earliest diamond after that in degree one occurs in degree 2q1, where q is a power of the characteristic. This paper is a contribution to an ongoing classification project of this subclass of thin Lie algebras. Specifically, we prove that the degree of the earliest diamond of finite type in such a Lie algebra can only attain certain values, which occur in explicit examples constructed elsewhere. Keywords: Modular Lie algebras, graded Lie algebras, central extensions, finitely presented Lie algebras, loop algebras. MSC: 17B50; 17B70, 17B65, 17B56 [ Fulltextpdf (218 KB)] for subscribers only. 