A skew brace is a set with two groups structure connected each other with an "odd" distributivity. They appears in the study of the Yang- Baxter equation, an equation from statistichal mechanics that shows up when discussing knot theory and braid groups. The aim of the thesis is to describe the main properties of skew braces and study their connection with solutions of Yang-Baxter equation. Moreover, we give an explicit construction of the free skew brace over a set.

A skew brace is a set with two groups structure connected each other with an "odd" distributivity. They appears in the study of the Yang- Baxter equation, an equation from statistichal mechanics that shows up when discussing knot theory and braid groups. The aim of the thesis is to describe the main properties of skew braces and study their connection with solutions of Yang-Baxter equation. Moreover, we give an explicit construction of the free skew brace over a set.

### Yang-Baxter Equation and Category of Skew Braces

#### Abstract

A skew brace is a set with two groups structure connected each other with an "odd" distributivity. They appears in the study of the Yang- Baxter equation, an equation from statistichal mechanics that shows up when discussing knot theory and braid groups. The aim of the thesis is to describe the main properties of skew braces and study their connection with solutions of Yang-Baxter equation. Moreover, we give an explicit construction of the free skew brace over a set.
##### Scheda Scheda DC
2021
Yang-Baxter Equation and Category of Skew Braces
A skew brace is a set with two groups structure connected each other with an "odd" distributivity. They appears in the study of the Yang- Baxter equation, an equation from statistichal mechanics that shows up when discussing knot theory and braid groups. The aim of the thesis is to describe the main properties of skew braces and study their connection with solutions of Yang-Baxter equation. Moreover, we give an explicit construction of the free skew brace over a set.
Skew Braces
Yang-Baxter Equation
Free Skew Brace
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.12608/32743`