Group schemes and rigidity of algebras in positive characteristic

Abstract

AbstractRigidity criteria for a finite dimensional associative or Lie algebra of positive characteristic are given. A geometrically rigid algebra may have deformations with nontrivial infinitesimals which may be interpreted as obstructions to integrating infinitesimal automorphisms. A group scheme theoretic nature of those obstructions is revealed. For each affine group scheme G of finite type over the ground field an invariantly defined G-module Obs(G) is introduced and formal properties of the functor GObs(G) are studied