Semisimplicity criteria for irreducible Hopf algebras in positive characteristic

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dc.creatorMasuoka, Akira
dc.date2008-12-22
dc.date.accessioned2026-07-07T12:21:12Z
dc.date.available2026-07-07T12:21:12Z
dc.descriptionWe 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.
dc.description8 pages; to appear in the Proc. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/0812.4115
dc.identifierhttp://arxiv.org/abs/0812.4115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213290
dc.subjectRings and Algebras
dc.subject16W30
dc.titleSemisimplicity criteria for irreducible Hopf algebras in positive characteristic
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