A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra

Mattarei, Sandro (2009) A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra. Israel Journal of Mathematics, 171 (1). pp. 1-14. ISSN 0021-2172

Full content URL: http://dx.doi.org/10.1007/s11856-009-0036-7

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Item Type:Article
Item Status:Live Archive

Abstract

A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements of N_p. Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥ (p − 1)^{1/p} (q − 1)^{1−1/(2p)}, necessarily belongs to N_p. This extends its special case for p = 2 which was proved in a previous paper by a different method.

Keywords:Lie algebra, injective derivation
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:18504
Deposited On:11 Dec 2015 09:09

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