Abstract:We consider homological finiteness properties FP n of certain Ngraded Lie algebras. After proving some general results, see Theorem A, Corollary B and Corollary C, we concentrate on a family that can be considered as the Lie algebra version of the generalized Bestvina-Brady groups associated to a graph Γ. We prove that the homological finiteness properties of these Lie algebras can be determined in terms of the graph in the same way as in the group case.
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