Semisimplicity criteria for irreducible Hopf algebras in positive characteristic

Akira Masuoka

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arXiv · 0812.4115

Semisimplicity criteria for irreducible Hopf algebras in positive characteristic

Akira Masuoka

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Abstract

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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BibTeX RIS

Akira Masuoka. 2008-12-22. Semisimplicity criteria for irreducible Hopf algebras in positive characteristic. https://arxiv.org/abs/0812.4115

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