Palindromic automorphisms of right-angled Artin groups

TL;DR

This paper introduces the palindromic automorphism group of right-angled Artin groups, explores its algebraic relations, and provides finite generating sets and conditions for its subgroups.

Contribution

It defines the palindromic automorphism and Torelli groups for right-angled Artin groups, linking them to known algebraic and geometric structures, and determines their generators and relations.

Findings

Finite generating sets for the palindromic automorphism group

Conditions when the palindromic automorphism group coincides with its centraliser

Generators for the palindromic Torelli group

Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group A_G. The palindromic automorphism group Pi A_G is related to the principal congruence subgroups of GL(n,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_G). We obtain finite generating sets for Pi A_G and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.