Quasitriangular $K$ -bimonoid

A quasitriangular $K$ -bimonoid is a $K$ -bimonoid $H$ equipped with an invertible element $𝑅 \in (H \otimes H) \times$ called the universal $R$ -matrix, such that #m/def/hopf

𝑅 Δ (𝑥) = Δ o p (𝑥) 𝑅, (Δ \otimes H) 𝑅 = 𝑅 13 𝑅 23, (H \otimes Δ) 𝑅 = 𝑅 13 𝑅 12

which in strings says

Such an element satisfies the Yang-Baxter equation

𝑅 12 𝑅 13 𝑅 23 = 𝑅 23 𝑅 13 𝑅 12

which in strings says

Proof

#missing/proof

Properties

Tracelike from an $R$ -matrix

#state/develop | #lang/en | #SemBr

Quasitriangular K-bimonoid

Properties

Quasitriangular $K$ -bimonoid