Right Angled Artin Groups and partial commutation, old and new
Group Theory
2020-05-14 v2
Abstract
We compute the -central and exponent- series of all right angled Artin groups, and compute the dimensions of their subquotients. We also describe their associated Lie algebras, and relate them to the cohomology ring of the group as well as to a partially commuting polynomial ring and power series ring. We finally show how the growth series of these various objects are related to each other.
Cite
@article{arxiv.1904.12151,
title = {Right Angled Artin Groups and partial commutation, old and new},
author = {Laurent Bartholdi and Henrika Härer and Thomas Schick},
journal= {arXiv preprint arXiv:1904.12151},
year = {2020}
}
Comments
v3: updated name of author (Henrike H\"arer, n\'ee Runde), improved exposition with more details of several proofs. Added remark on homology gradient computation