# nLab reflection equation algebra

## Reflection Equation

Given a solution $R$ of the Yang-Baxter equation, the reflection equation (with additive spectral parameter) reads

$R(u-v) K_1 (u) R(u+v) K_2 (v) = K_2 (v) R(u+v) K_1 (u) R(u-v)$

## 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 $U_q(gl(n))$-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; doi hep-th/9402051; Reflection equation and link polynomials for arbitrary genus solid tori, hep-th/9301023