Yangian for cotangent Lie algebras and spectral $R$-matrices
Yangian for cotangent Lie algebras and spectral $R$-matrices
In this paper, we present a canonical quantization of Lie bialgebra structures on the formal power series $\mathfrak{d}[\![t]\!]$ with coefficients in the cotangent Lie algebra $\mathfrak{d} = T^*\mathfrak{g} = \mathfrak{g} \ltimes \mathfrak{g}^*$ to a simple complex Lie algebra $\mathfrak{g}$. We prove that these quantizations produce twists to the natural analog …