Local rigidity of weak or no hyperbolicity algebraic actions

Abstract

In this paper we study rigidity properties of abelian \hyphenation{break-able}actions with weak or no hyperbolicty. We introduce a general strategy for proving $C^{\infty }$ local rigidity of algebraic actions. As a consequence, we show $C^{\infty }$ local rigidity for a broad class of parabolic algebraic actions on homogeneous spaces of semisimple Lie groups. This is the first time in the literature that (strong) local rigidity for these actions is addressed.

arXiv admin note: text overlap with arXiv:1908.09181