Pseudo-Riemannian Lie algebras with coisotropic ideals and integrating the Laplace-Beltrami equation on Lie groups

A. A. Magazev, I. V. Shirokov

We identify a class of left-invariant pseudo-Riemannian metrics on Lie groups for which the Laplace-Beltrami equation reduces to a first-order PDE and admits exact solutions. The d…