Graded Lie algebras of maximal class. III
type: Item
instance of: scholarly article
title: Graded Lie algebras of maximal class. III
zbMATH Open document ID: 1058.17020
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: \textit{M. F. Newman} and the reviewer have classified [J. Algebra 229, No. 2, 750--784 (2000; Zbl 0971.17015)] graded Lie algebras of maximal class (generated by elements of weight one) in odd characteristic. This builds upon work of \textit{C. Carrara} [Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4, No. 2, 391--427 (2001)] and \textit{M. F. Newman}, \textit{S. Mattarei} and the reviewer [Trans. Am. Math. Soc. 349, No. 10, 4021--4051 (1997; Zbl 0895.17031)]. The basic elements for constructing these algebras are provided by the algebras constructed by \textit{A. Shalev} [Arch. Math. 63, No. 4, 297--301 (1994; Zbl 0803.17006)] as the positive parts of certain twisted loop algebras of some finite-dimensional, modular, simple Lie algebras of Hamiltonian type. In the paper under review, the author extends the classification to the case of characteristic two. The main novelty with respect to the odd characteristic case is that another basic element is needed here, namely a new class of finite-dimensional, modular, simple Lie algebras in characteristic two, which has been constructed by the author [J. Algebra 271, No. 2, 454--481 (2004; Zbl 1054.17007)].
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 2153310
zbMATH Keywords: graded Lie algebras
zbMATH Keywords: modular Lie algebras
zbMATH Keywords: graded Lie algebras of maximal class
author: Giuseppe Jurman
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.11.006
OpenAlex ID: W3022632743
Wikidata QID: Q57314677
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DOI: 10.1016/J.JALGEBRA.2004.11.006
description: scientific article; zbMATH DE number 2153310