Narrow lie algebras: A coclass theory and a characterization of the Witt algebra

Aner Shalev*, Efim I. Zelmanov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

In this paper we examine some narrowness conditions for Lie algebras over a fieldFof characteristic zero. In particular we show that the natural analogs of the main coclass conjectures forp-groups hold in the context of N-graded Lie algebrasLwhich are generated by their first homogeneous componentL1. While Lie algebras of finite coclass need not be soluble, we show that the positive part of the Witt algebra DerF[x] is the only non-soluble N-graded Lie algebraLof coclass 1 which is generated byL1andL2.

Original languageAmerican English
Pages (from-to)294-331
Number of pages38
JournalJournal of Algebra
Volume189
Issue number2
DOIs
StatePublished - 15 Mar 1997

Bibliographical note

Funding Information:
* Supported by the Bi-National Science Foundation United States—Israel, Grant 92-00034.

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