Construction of a group of automorphisms for an infinite family of Garside groups

The structure groups of non-degenerate symmetric set-theoretical solutions of the quantum Yang-Baxter equation provide an infinite family of Garside groups with many interesting properties. Given a non-degenerate symmetric solution, we construct for its structure group a group of automorphisms. Moreover, we show this group of automorphisms admits a subgroup that preserves the Garside properties of the structure group. In some cases, we could also prove the group of automorphisms obtained is an outer automorphism group.