- Date
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Tuesday 17 December 2024, 14.00 - 14.30
- Abstract
- Recall that a set-theoretic solution of the Yang-Baxter equation is a tuple $(X,r)$, where $X$ is a non-empty set and $r: X \times X \rightarrow X \times X$ a bijective map such that $$(r \times id_X ) (id_X \times r) (r \times id_X) = (id_X \times r) (r \times id_X ) (id_X \times r),$$ where one denotes $r(x,y)=(\lambda_x(y), \rho_y(x))$. Attention is often restricted to so-called non-degenerate solutions, i.e. $\lambda_x$ and $\rho_y$ are bijective. We will call these solutions for short in the remainder of this abstract. To understand more general objects, it is an important technique to study 'minimal' objects and glue these together. For solutions both indecomposable and simple solutions fit the bill for being a minimal object. In this talk we will report on recent work with I. Colazzo. We discuss the extension of a method to construct new indecomposable or simple solutions.
