Hypoellipticity for a sum of complex squares (Q2895190)

The author surveys a result obtained in collaboration with \textit{A. Bove} and \textit{D. S. Tartakoff} [in: Complex analysis. Several complex variables and connections with PDE theory and geometry. Proceedings of the conference in honour of Linda Rothschild, Fribourg, Switzerland, July 7--11, 2008. Basel: Birkhäuser. 51--73 (2010; Zbl 1201.35092)] where an example is given of a sum of squares of complex vector fields in two variables that fails to be hypoelliptic, and yet satisfies the Hörmander bracket condition (in the sense that their Lie algebra generates the complexified tangent space at any given point).NEWLINENEWLINEFor the entire collection see [Zbl 1205.35004].