Andrey Mudrov

Extended Jordanian twists for Lie algebras

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element F, universal R-matrix and the corresponding canonical element T. It is shown that the twisted Hopf algebra UF(B∨) is self-dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld–Jimbo quantization to the Jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.

Explicit Equivariant Quantization on Coadjoint Orbits of GL(n, C)

We present an explicit Uh(gl(n, C))-equivariant quantization on coadjoint orbits of GL(n, C). It forms a two-parameter family quantizing the Poisson pair of the reflection equation and Kirillov–Kostant–Souriau brackets.

Reflection equation, twist, and equivariant quantization

AbstractWe prove that the reflection equation (RE) algebraLR associated with a finite dimensional representation of a quasitriangular Hopf algebraH is twist-equivalent to the corresponding Faddeev-Reshetikhin-Takhtajan (FRT) algebra. We show thatLR is a module algebra over the twisted tensor square

Baxterization of Solutions to Reflection Equation with Hecke R-matrix

{\mathcal{H}}\mathop \otimes \limits^{\mathcal{R}} {\mathcal{H}}

Twisting Adjoint Module Algebras

and the double D(

Reflection equation and twisted Yangians

{\mathcal{H}}