Generalized electrical Lie algebras

My talk is based on joint work with Azat Gainutdinov and Vassily Gorbounov, in which we generalize in several ways the electrical Lie algebras originally introduced by Lam and Pylyavskyy. To each semisimple or Kac-Moody Lie algebra g we associate a family of flat deformations of its nilpotent part parametrized by the points of the Cartan subalgebra of g. If g=sl_n, then the generic electrical Lie algebra is sp_{n-1}, which is simple if n is odd. A similar situation occurs with other classical Lie algebras: for instance, if g=sp_{2n}, then its generic electrical Lie algebra is sp_n \oplus sp_{n-1}, which is never semisimple. 

If time permits, I will explain the electrical invariants in g-modules and ``edge models" of electrical Lie algebras in semisimple and affine case, where the deformation parameters can be viewed as edge weights of the Dynkin diagram of g.