Nilpotency, Solvability and Frattini Theory for Poisson algebras

Abstract: This paper shows that a Poisson algebra is nilpotent if and only if it is both associative and Lie nilpotent and examines various properties of the nilradical and the solvable radical. It introduces a basic Frattini theory for dialgebras and then investigates a more detailed theory for Poisoon algebras.