Semisimplicity criteria for irreducible Hopf algebras in positive characteristic
Masuoka, Akira
Original · EN
We prove that a finite-dimensional irreducible Hopf algebra H in positive characteristic is semisimple, if and only if it is commutative and semisimple, if and only if the restricted Lie algebra P(H) of the primitives is a torus. This generalizes Hochschild's theorem on restricted Lie algebras, and also generalizes Demazure and Gabriel's and Sweedler's results on group schemes, in the special but essential situation with finiteness assumption added.
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