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Nilpotent-by-abelian Lie algebras of type FPm
Published online by Cambridge University Press: 10 February 2010
Abstract
Let L be a finitely generated Lie algebra which is a split extension of a free nilpotent Lie algebra N by a finite dimensional abelian Lie algebra. Let V denote the quotient of N by its commutator subalgebra; we can regard V as a module for L/N. We discuss the relationship between the homological finiteness properties of V and those of L. In particular, we show that if L has type FPm and N has class c then V is 1 + c(m − 1)-tame (equivalently, the (1 + c(m − 1))th tensor power of V is finitely generated under the diagonal action of L/N).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 3 , May 2010 , pp. 429 - 437
- Copyright
- Copyright © Cambridge Philosophical Society 2010