# Algebraic invariants for right-angled Artin groups

@article{Papadima2005AlgebraicIF,
title={Algebraic invariants for right-angled Artin groups},
author={Stefan Papadima and Alexander I. Suciu},
journal={Mathematische Annalen},
year={2005},
volume={334},
pages={533-555}
}
• Published 29 December 2004
• Mathematics
• Mathematische Annalen
A finite simplicial graph Γ determines a right-angled Artin group GΓ, with generators corresponding to the vertices of Γ, and with a relation υw=wυ for each pair of adjacent vertices. We compute the lower central series quotients, the Chen quotients, and the (first) resonance variety of GΓ, directly from the graph Γ.
An introduction to right-angled Artin groups
Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical
• Mathematics
• 2007
Bestvina–Brady groups arise as kernels of length homomorphisms GΓ → ℤ from right‐angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ΔΓ, we compute several
Homology of subgroups of right-angled Artin groups
We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew)
Moment-angle Complexes, Monomial Ideals and Massey Products
• Mathematics
• 2007
Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of
• Mathematics
• 2006
A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The
Graph braid groups and right-angled Artin groups
• Mathematics
• 2008
We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $\ge 5$. In order to have the necessity part, graphs are organized into
Pure virtual braids, resonance, and formality
• Mathematics
• 2016
We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer
Edge stabilization in the homology of graph braid groups
• Mathematics
Geometry & Topology
• 2020
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homology by the

## References

SHOWING 1-10 OF 47 REFERENCES
• Mathematics
• 2007
Bestvina–Brady groups arise as kernels of length homomorphisms GΓ → ℤ from right‐angled Artin groups to the integers. Under some connectivity assumptions on the flag complex ΔΓ, we compute several
Morse theory and finiteness properties of groups
• Mathematics
• 1997
Abstract. We examine the finiteness properties of certain subgroups of “right angled” Artin groups. In particular, we find an example of a group that is of type FP(Z) but is not finitely presented.
The Hilbert Series of the Face Ring of a Flag Complex
It is shown that the Hilbert series of the face ring of a clique complex of a graph G is, up to a factor, just a specialization of , the subgraph polynomial of the complement of G, which yields a formula for the h-vector of the flag complex in terms of those two invariants of .
The Bieri–Neumann–Strebel Invariants for Graph Groups
• Mathematics
• 1993
Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is the group with generators in one-to-one correspondence with the vertices of ${\cal G}$ and with relations stating two
Koszul Algebras from Graphs and Hyperplane Arrangements
• Mathematics
• 1997
This work was started as an attempt to apply theory from noncommutative graded algebra to questions about the holonomy algebra of a hyperplane arrangement. We soon realized that these algebras and
Koszul homology and Lie algebras with application to generic forms and points
• Mathematics
• 2001
We study the Koszul dual for general superalgebras, and apply it to the Koszul homology of a graded algebra. We show that a part of the Koszul homology algebra is related to the homotopy Lie algebra
Hyperplane arrangement cohomology and monomials in the exterior algebra
• Mathematics
• 1999
We show that if X is the complement of a complex hyperplane arrangement, then the homology of X has linear free resolution as a module over the exterior algebra on the first cohomology of X. We study
Cohomology of the Orlik–Solomon Algebras and Local Systems
• Mathematics
Compositio Mathematica
• 2000
The paper provides a combinatorial method to decide when the space of local systems with nonvanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has
The lower central series of the free partially commutative group
• Mathematics
• 1992
This paper is devoted to the study of the lower central series of the free partially commutative groupF(A, ϑ) in connection with the associated free partially commutative Lie algebra. Using a