Construction of a group of automorphisms for an infinite family of Garside groups
Abstract
The structure groups of nondegenerate symmetric settheoretical solutions of the quantum YangBaxter equation provide an infinite family of Garside groups with many interesting properties. Given a nondegenerate 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 DOI:
 10.48550/arXiv.1411.1189
 arXiv:
 arXiv:1411.1189
 Bibcode:
 2014arXiv1411.1189C
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Quantum Algebra
 EPrint:
 Communications in Algebra (2018), vol. 46 (11), 47104723