Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V

Abstract

We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLₙ(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp₂ₙ(q), PΩ⁺₄ₙ, PΩ⁻₄ₙ, ³D₄(q), E₇(q), E₈(q), F₄(q), or G₂(q) with q even is the group algebra.