Involutive Yang-Baxter: cabling, decomposability, Dehornoy class
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916173602357248 |
|---|---|
| author | Lebed, V. Ramírez, S. Vendramin, L. |
| author_facet | Lebed, V. Ramírez, S. Vendramin, L. |
| contents | We develop new machinery for producing decomposability tests for involutive solutions to the Yang-Baxter equation. It is based on the seminal decomposability theorem of Rump, and on "cabling" operations on solutions and their effect on the diagonal map. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-More and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the braces language) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garside-theoretic approach to involutive solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02041 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Involutive Yang-Baxter: cabling, decomposability, Dehornoy class Lebed, V. Ramírez, S. Vendramin, L. Quantum Algebra Group Theory Rings and Algebras 16T25, 17D99, 08A05 We develop new machinery for producing decomposability tests for involutive solutions to the Yang-Baxter equation. It is based on the seminal decomposability theorem of Rump, and on "cabling" operations on solutions and their effect on the diagonal map. Our machinery yields an elementary proof of a recent decomposability theorem of Camp-More and Sastriques, as well as original decomposability results. It also provides a conceptual interpretation (using the braces language) of the Dehornoy class, a combinatorial invariant naturally appearing in the Garside-theoretic approach to involutive solutions. |
| title | Involutive Yang-Baxter: cabling, decomposability, Dehornoy class |
| topic | Quantum Algebra Group Theory Rings and Algebras 16T25, 17D99, 08A05 |
| url | https://arxiv.org/abs/2209.02041 |