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

[摘要] 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 N-graded Lie algebras L which are generated by their first homogeneous component L(1). While Lie algebras of finite coclass need not be soluble, we show that the positive part of the Witt algebra Der F[x] is the only non-soluble N-graded Lie algebra L of coclass 1 which is generated by L(1) and L(2). (C) 1997 Academic Press.

[发布日期] 1997-03-15