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Cabling techniques for bijective solutions of the Yang–Baxter equation
- Speaker(s)
- University of Leeds
- Affiliation
- University of Leeds
- Language of the talk
- English
- Date
- Nov. 28, 2024, 12:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- referat online
- Seminar
- Seminar Algebra
In this talk, we introduce a definition of cabling for bijective non-degenerate set-theoretic solutions to the Yang–Baxter equation, with a focus on indecomposability. We examine fundamental differences between involutive and non-involutive solutions, particularly that involutive solutions naturally embed into solutions associated with their structure group, while this embedding often fails for non-involutive cases. To address this, we connect the decomposability of solutions with that of their injectivization. A core result we prove is that cabling preserves morphisms, ensuring that simplicity and indecomposability are maintained under suitable cabling. Our methods not only extend the theorems of Lebed, Ramírez, and Vendramin to non-involutive solutions but also provide numerical criteria for indecomposability. This talk is based on joint work with A. Van Antwerpen.
