An algorithmic construction of group automorphisms and the quantum Yang-Baxter equation

ABSTRACT

The structure group G of a non-degenerate symmetric set (X,S) is a Bieberbach and a Garside group. We describe a combinatorial method to compute explicitly a group of automorphisms of G and show this group admits a subgroup that preserves the Garside structure. In some special cases, we could also prove the group of automorphisms found is an outer automorphism group.

KEYWORDS:

• Bieberbach group
• bijective cocycle
• Garside groups
• group of automorphisms
• outer automorphism group
• quantum groups
• set-theoretical solution of the quantum Yang-Baxter equation

AMS SUBJECT CLASSIFICATION:

• 16T25
• 20F36

Acknowledgment

I am very grateful to Arye Juhasz and Yuval Ginosar for fruitful discussions and to the referee for the comments.