A note on Masuoka's Theorem for semisimple irreducible Hopf algebras

Abstract

Masuoka proved (2009) that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple if and only if it is commutative semisimple if and only if the Hopf subalgebra generated by all primitives is semisimple. In this paper, we give another proof of this result by using Hochschild cohomology of coalgebras.

9 pages; to appear in Archiv der Mathematik

References in corpus (1)

• Connected Hopf Algebras of Dimension $p^2$

Cited by in corpus (2)

• Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristic
• Primitive Deformations of Quantum $p$-groups