On the homological finiteness properties of some modules over metabellian Lie algebras
Identifieur interne : 001079 ( Main/Exploration ); précédent : 001078; suivant : 001080On the homological finiteness properties of some modules over metabellian Lie algebras
Auteurs : Dessislava H. Kochloukova [Brésil]Source :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2002-12-01.
Abstract
Abstract: We characterise the modulesB of homological typeFP m over a finitely generated Lie algebraL such thatL is a split extension of an abelian idealA and an abelian subalgebraQ andA acts trivially onB. The characterisation is in terms of the invariant Δ introduced by R. Bryant and J. Groves and is a Lie algebra version of the generalisation [K 4, conjecture 1] of the still openFP m -Conjecture for metabelian groups [Bi-G, Conjecture p. 367]. The casem=1 of our main result is treated separately, as there the characterisation is proved without restrictions on the type of the extension.
Url:
DOI: 10.1007/BF02773165
Affiliations:
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