Generalized Gaudin spin chains, nonskew symmetric r-matrices, and reflection equation algebras

摘要

Using a one-parametric family of automorphisms sigma(u) of finite-dimensional simple Lie algebras g and classical skew-symmetric r-matrices r(12)(u-v), we construct "twisted" nonskew symmetric classical r-matrices r(12)(sigma)(u,v) with spectral parameters. We show that in the special case sigma(u)=Ad(K(u)) and classical matrix Lie algebras g, they are connected with the quasiclassical limit of the reflection equation algebras. Using them and results of our previous papers, we construct new integrable quantum spin chains of the "generalized Gaudin" type with an arbitrary value of spin living at each site. (c) 2007 American Institute of Physics.