NARROW LIE-ALGEBRAS - A COCLASS THEORY AND A CHARACTERIZATION OF THE WITT ALGEBRA

In this paper we examine some narrowness conditions for Lie algebras o ver a field F of characteristic zero. In particular we show that the n atural analogs of the main coclass conjectures for p-groups hold in th e context of N-graded Lie algebras L which are generated by their firs t homogeneous component L(1). While Lie algebras of finite coclass nee d not be soluble, we show that the positive part of the Witt algebra D er F[x] is the only non-soluble N-graded Lie algebra L of coclass 1 wh ich is generated by L(1) and L(2). (C) 1997 Academic Press.