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.
- Pub Date:
- October 2015
- Mathematics - Group Theory;
- Mathematics - Geometric Topology
- 20 pages, 2 figures. Version 2: corrected proof of Proposition 3.1, other minor changes as suggested by referee. To appear in Groups Geom. Dyn