Thin loop algebras of Albert–Zassenhaus algebras

Avitabile, Marina and Mattarei, Sandro (2007) Thin loop algebras of Albert–Zassenhaus algebras. Journal of Algebra, 315 (2). pp. 824-851. ISSN 0021-8693

Full content URL: http://dx.doi.org/10.1016/j.jalgebra.2007.03.001

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Item Type:Article
Item Status:Live Archive

Abstract

Thin Lie algebras are Lie algebras over a field, graded over the positive integers and satisfying a certain narrowness condition. In particular, all homogeneous components have dimension one or two, and are called diamonds in the latter case. The first diamond is the component of degree one, and the second diamond can only occur in degrees 3, 5, q or 2q−1, where q is a power of the characteristic of the underlying field. Here we consider several classes of thin Lie algebras with second diamond in degree q. In particular, we identify the Lie algebras in one of these classes with suitable loop algebras of certain Albert–Zassenhaus Lie algebras. We also apply a deformation technique to recover other thin Lie algebras previously produced as loop algebras of certain graded Hamiltonian Lie algebras.

Keywords:Algebra
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18508
Deposited On:28 Dec 2016 20:44

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