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Narrow Lie Algebras: A Coclass Theory and a Characterization of the Witt Algebra

✍ Scribed by Aner Shalev; Efim I. Zelmanov

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
396 KB
Volume
189
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we examine some narrowness conditions for Lie algebras over a field F of characteristic zero. In particular we show that the natural analogs of the main coclass conjectures for p-groups hold in the context of ‫-ήŽβ€¬graded Lie algebras L which are generated by their first homogeneous component L . While Lie 1 algebras of finite coclass need not be soluble, we show that the positive part of the w x Witt algebra Der F x is the only non-soluble ‫-ήŽβ€¬graded Lie algebra L of coclass 1 which is generated by L and L .

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