Given a solution of the Yang-Baxter equation, the reflection equation (with additive spectral parameter) reads
References
Dimitri Gurevich, Pavel Pyatov, Pavel Saponov, Reflection equation algebra in braided geometry, Journal of Generalized Lie Theory and Applications 2 (2008), No. 3, 162–174 pdf
P. P. Kulish, Reflection equation algebras and quantum groups, in: Quantum and Non-Commutative Analysis, Mathematical Physics Studies 16 (1993) 207-220 doi
A. Mudrov, Characters of -Reflection Equation Algebra, Lett. Math. Phys. 60:3, 283-291 (2002) doi
Christian Schwiebert, Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials, J. Math. Physics 02/1994; doihep-th/9402051; Reflection equation and link polynomials for arbitrary genus solid tori, hep-th/9301023
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