Set-theoretic Yang–Baxter & reflection equations and quantum group symmetries

Connections between set-theoretic Yang-Baxter and reflection equations quantum integrable systems are investigated. We show that $R$-matrices expressed as twists of known solutions. then focus on twisted algebras we derive the associated defining algebra relations for being Baxterized solutions $A$-type Hecke ${\cal H}_N(q=1)$. in case there exists a ``boundary'' finite sub-algebra some special choice elements $B$-type B}_N(q=1, Q)$. also key proposition double row transfer matrix is essentially terms algebra. This one fundamental results this investigation together with proof duality boundary subalgebra These universal statements largely generalize previous relevant findings, allow symmetries matrix.