Abstract
We consider the structure group of a non-degenerate symmetric (non-trivial) set-theoretical solution of the quantum Yang-Baxter equation. This is a Bieberbach group and also a Garside group. We show this group is not bi-orderable, that is it does not admit a total order which is invariant under left and right multiplications. Regarding the existence of a left invariant total ordering, there is a great diversity. There exist structure groups with a recurrent left order and with space of left orders homeomorphic to the Cantor set, while there exist others that are even not unique product groups.
Original language | English |
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Pages (from-to) | 1349-1359 |
Number of pages | 11 |
Journal | International Journal of Algebra and Computation |
Volume | 26 |
Issue number | 7 |
DOIs | |
State | Published - 1 Nov 2016 |
Bibliographical note
Publisher Copyright:© 2016 World Scientific Publishing Company.
Keywords
- Garside groups
- local indicability
- orderability of groups
- set-theoretical solutions of the quantum Yang-Baxter equation
- unique product property
ASJC Scopus subject areas
- General Mathematics