Symmetry group methods for heat kernels

We apply methods of symmetry groups to heat equations on R with drift terms and to heat equations for Lie groups. In particular, we are able to characterize those functions f for which equations of the form (partial derivative (2)u/partial derivativex(2)) + f(x)u(x) = u(t) have a point symmetry which takes a constant solution to the fundamental solution. Further, we apply symmetry methods to the heat equation of the ax + b group. (C) 2001 American Institute of Physics.