Fibered rotation vector and hypoellipticity for quasi‐periodic cocycles in compact Lie groups.

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi‐periodic cocycles in Td×G, G a compact Lie group, over a Diophantine rotation. We then prove that if this rotation vector is Diophantine with respect to the rotation in Td, the cocycle is smoothly reducible, thus establishing a hypoellipticity property in the spirit of the Greenfield–Wallach conjecture in PDEs. [ABSTRACT FROM AUTHOR]