# Palindromic automorphisms of right-angled Artin groups

### Neil J. Fullarton

Rice University, Houston, USA### Anne Thomas

University of Sydney, Australia

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## Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group $A_\Gamma$. The palindromic automorphism group $\Pi A_\Gamma$ is related to the principal congruence subgroups of GL$(n,\mathbb Z)$ and to the hyperelliptic mapping class group of an oriented surface, and sits inside the centraliser of a certain hyperelliptic involution in Aut$(A_\Gamma)$. We obtain finite generating sets for $\Pi A_\Gamma$ and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.

## Cite this article

Neil J. Fullarton, Anne Thomas, Palindromic automorphisms of right-angled Artin groups. Groups Geom. Dyn. 12 (2018), no. 3, pp. 865–887

DOI 10.4171/GGD/458