Hodge decomposition on stratified Lie groups (Q1077024)

The classical Hodge decomposition theorem states that on a compact Riemannian manifold every p-form \(\alpha\) can be written as \(\alpha =\alpha_ 1+\alpha_ 2+\alpha_ 3\), where \(\alpha_ 1=d^*\beta_ 1\), \(\alpha_ 2=d\beta_ 2\) and \(\alpha_ 3\) is harmonic. In this paper a considerable extension of the Hodge theorem is presented, namely the theorem is proved in the general setting of stratified groups. The necessary background on CR-structures and Heisenberg groups is also explained in an easy-to-read form. A valuable contribution to an important subject!