Charmenability of higher rank arithmetic groups

We complete the study of characters on higher rank semisimple lattices initiated in [BH21, BBHP22], missing case being simple algebraic groups arbitrary characteristics. More precisely, we investigate dynamical properties conjugation action such their space positive definite functions. Our main results deal with existence and classification from which derive applications to topological dynamics, ergodic theory, unitary representations operator algebras. key theorem is an extension noncommutative Nevo–Zimmer structure obtained [BH21] defined over local fields. also deduce a analogue Margulis’ factor for von Neumann subalgebras Poisson boundary arithmetic groups.