Coabelian ideals in \ℕ-graded Lie algebras and applications to\n right angled Artin Lie algebras

2020/06/04 by Dessislava H. Kochloukova, Kochloukova, Dessislava H., Conchita Martı́nez-Pérez +1
Mathematics · #16S30 #20J05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2006.02883

openalex publication_date 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider homological finiteness properties FP_n of certain\n\ℕ-graded Lie algebras. After proving some general results, see\nTheorem A, Corollary B and Corollary C, we concentrate on a family that can be\nconsidered as the Lie algebra version of the generalized Bestvina-Brady groups\nassociated to a graph \Γ. We prove that the homological finiteness\nproperties of these Lie algebras can be determined in terms of the graph in the\nsame way as in the group case. In the last version we have corrected some\nmissprints, in particular the statement of Theorem D (from n-1-acyclicity to\nn-1 - |w|-acyclicity).\n

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