On the Sigma-invariants of even Artin groups of FC-type

Blasco-García, Rubén; Cogolludo-Agustín, José Ignacio; Martı́nez-Pérez, Conchita

doi:10.1016/j.jpaa.2021.106984

Cited by 5 publications

(17 citation statements)

References 22 publications

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“…In the following result we use homological methods to classify when those ideals are of type FP n . A similar computation for Bestvina-Brady groups can be found in [12] and for cocyclic normal subgroups of certain Artin groups in [6].…”

Section: Only If For Every Lie Subalgebra N Of L Of Codimension One S...mentioning

confidence: 69%

“…On other hand for x s ∈ V (Γ) V (Γ χ ) we have that χ(x s ) = 0 and there is a vertex v i, j ∈ V (Γ χ ) such that there is an edge between x s and v i, j . Then [v i, j , x s ] = 0, hence by (6) [λ i, j x 1 + ∑ 2≤t≤ j λ i, j,t y i,t , x s ] = 0. Then (8) [x 1 , x s ] ∈ {y i,t , x s } i,t,s .…”

Section: Elementary Approach For Finite Generation Of I χmentioning

confidence: 99%

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Coabelian ideals in $\mathbb{N}$-graded Lie algebras and applications to right angled Artin Lie algebras

Kochloukova¹,

Martı́nez-Pérez²

2020

Preprint

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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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Section: Only If For Every Lie Subalgebra N Of L Of Codimension One S...mentioning

confidence: 69%

Section: Elementary Approach For Finite Generation Of I χmentioning

confidence: 99%

Coabelian ideals in $\mathbb{N}$-graded Lie algebras and applications to right angled Artin Lie algebras

Kochloukova¹,

Martı́nez-Pérez²

2020

Preprint

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“…A key result we will be using to compute the Σ-invariants of the spherical irreducible Artin groups is the following. Moreover, as in [9,28] and [29], many of our results will be based on the next theorem, together with the action on the Deligne complex. Theorem 2.5 [28,Theorem 3.2].…”

Section: 𝚺-Invariantsmentioning

confidence: 99%

On the Σ$\Sigma$‐invariants of Artin groups satisfying the K(π,1)$K(\pi,1)$‐conjecture

Escartín‐Ferrer,

Martínez‐Perez

2024

Journal of London Math Soc

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We consider ‐invariants of Artin groups that satisfy the ‐conjecture. These invariants determine the cohomological finiteness conditions of subgroups that contain the derived subgroup. We extend a known result for even Artin groups of FC‐type, giving a sufficient condition for a character to belong to . We also prove some partial converses. As applications, we prove that the ‐conjecture holds true when there is a prime that divides for any edge with even label , we generalize to Artin groups the homological version of the Bestvina–Brady theorem and we compute the ‐invariants of all irreducible spherical and affine Artin groups and triangle Artin groups, which provide a complete classification of the and properties of their derived subgroup.

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“…The case when G is a right-angled Artin group was settled by Meier-Meinert-VanWyk ( [30]) but for general Artin groups just some particular cases are known. For example, some Artin groups that are not RAAGs were considered by K. Almeida in [1] and some even Artin groups were considered by R. Blasco García, J. I. Cogolludo Agustín, C. Martínez Pérez in [9] and by D. Kochloukova in [25].…”

Section: Introductionmentioning

confidence: 99%