Classification of matched pairs of actions on H8 yields exactly six, two of which give involutive Yang-Baxter operators and are not derived from coquasitriangular structures.
Set-theoretic type solutions of the braid equation
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abstract
In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationships between set-theoretical solutions, q-cycle sets, q-braces, skew-braces, matched pairs of groups and invertible $1$-cocycles remain valid in our setting.
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Matched pairs of actions on the Kac-Paljutkin algebra $H_8$
Classification of matched pairs of actions on H8 yields exactly six, two of which give involutive Yang-Baxter operators and are not derived from coquasitriangular structures.