Matrix exponential groups and Kolmogorov-Fokker-Planck equations

Aim of this paper is to provide new examples of Hörmander operators L to which a Lie group structure can be attached making L left invariant. Our class of examples contains several subclasses of operators appearing in literature and arising both in theoretical and in applied fields: evolution Kolmogorov operators, degenerate Ornstein–Uhlenbeck operators, Mumford and Fokker–Planck operators, Ornstein–Uhlenbeck operators with time-dependent periodic coefficients. Our examples basically come from exponential of matrices, aswell as from linear constant-coefficient ODE’s, in R or in C. Furthermore, we describe how these groups can be combined together to obtain new structures and new operators, also having an interest in the applied field.