Report
Reflection equation as a tool for studying solutions to the Yang-Baxter equation
| العنوان: | Reflection equation as a tool for studying solutions to the Yang-Baxter equation |
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| المؤلفون: | Lebed, V., Vendramin, L. |
| المصدر: | J. Algebra 607 (2022), 360-380 |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematics - Group Theory |
| الوصف: | Given a right-non-degenerate set-theoretic solution $(X,r)$ to the Yang-Baxter equation, we construct a whole family of YBE solutions $r^{(k)}$ on $X$ indexed by its reflections $k$ (i.e., solutions to the reflection equation for $r$). This family includes the original solution and the classical derived solution. All these solutions induce isomorphic actions of the braid group/monoid on $X^n$. The structure monoids of $r$ and $r^{(k)}$ are related by an explicit bijective $1$-cocycle-like map. We thus turn reflections into a tool for studying YBE solutions, rather than a side object of study. In a different direction, we study the reflection equation for non-degenerate involutive YBE solutions, show it to be equivalent to (any of the) three simpler relations, and deduce from the latter systematic ways of constructing new reflections. Comment: 18 pages, 12 figures. Final version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2021.02.002 |
| URL الوصول: | http://arxiv.org/abs/2008.01752 |
| رقم الانضمام: | edsarx.2008.01752 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jalgebra.2021.02.002 |
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