Abstract
We consider homological finiteness properties FPn of certain ℕ-graded 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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Acknowledgements
During the preparation of this work the first named author was partially supported by CNPq grant 301779/2017-1 and by FAPESP grant 2018/23690-6. The second named author was partially supported by PGC2018-101179-B-I00 and by Grupo Álgebra y Geometría, Gobierno de Aragón and Feder 2014–2020 “Construyendo Europa desde Aragón”.
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Kochloukova, D.H., Martínez-Pérez, C. Coabelian Ideals in ℕ-graded Lie algebras and applications to right angled Artin Lie algebras. Isr. J. Math. 247, 797–829 (2022). https://doi.org/10.1007/s11856-021-2281-3
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DOI: https://doi.org/10.1007/s11856-021-2281-3