Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 19 (2009), No. 3, 483--505
Copyright Heldermann Verlag 2009

Diamonds of Finite Type in Thin Lie Algebras

Marina Avitabile
Dip. di Matematica e Applicazioni, UniversitÓ di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy

Sandro Mattarei
Dip. di Matematica, UniversitÓ di Trento, Via Sommarive 14, 38050 Povo, Italy

Borrowing some terminology from pro-p groups, thin Lie algebras are N-graded 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 2q-1, 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

[ Fulltext-pdf  (218  KB)] for subscribers only.