Journal of Lie Theory

no. 1
Diamonds of Finite Type in Thin Lie Algebras
Marina Avitabile1; Sandro Mattarei2
1Dip. di Matematica ed Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy
2Dip. di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38050 Povo, Italy
Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 185-207
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.
DOI: 10.5802/jolt.546
Classification: 17B50, 17B70, 17B65, 17B56
Keywords: Modular Lie algebras, graded Lie algebras, central extensions, finitely presented Lie algebras, loop algebras

Marina Avitabile  1 ; Sandro Mattarei  2

1 Dip. di Matematica ed Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy
2 Dip. di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38050 Povo, Italy 
Marina Avitabile; Sandro Mattarei. Diamonds of Finite Type in Thin Lie Algebras. Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 185-207. doi: 10.5802/jolt.546
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