We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

Castelli M.
;
Catino F.;Pinto G.
2019

Abstract

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/435227
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