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

Aner Shalev; Efim I. Zelmanov

doi:10.1006/jabr.1996.6819

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

Aner Shalev^*, Efim I. Zelmanov

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	294-331
Number of pages	38
Journal	Journal of Algebra
Volume	189
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1996.6819
State	Published - 15 Mar 1997

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

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10.1006/jabr.1996.6819

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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.",

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

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