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Irreducible finitary Lie algebras over fields of positive characteristic

Published online by Cambridge University Press:  01 July 2000

FELIX LEINEN  and
ORAZIO PUGLISI
FELIX LEINEN
Affiliation:
Fachbereich 17-Mathematik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany; e-mail: [email protected]
ORAZIO PUGLISI
Affiliation:
Dipartimento di Matematica, Università degli Studi di Trento, I-38050 Povo (Trento), Italy; e-mail: [email protected]
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Abstract

A Lie subalgebra L of [gfr ][lfr ][ ](V) is said to be finitary if it consists of elements of finite rank. We study the situation when L acts irreducibly on the infinite-dimensional vector space V and show: if Char [ ] > 7, then L has a unique minimal ideal I. Moreover I is simple and L/I is solvable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 1 , July 2000 , pp. 1 - 8
Copyright
2000 Cambridge Philosophical Society

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