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

2012/12/04 by Xingting Wang, Wang, Xingting
Mathematics · Physics and Astronomy · #16T05 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Commutative property #FOS: Mathematics #Hopf algebra #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Subalgebra #math.QA #math.RA #msc:16T05

paper · pdf · doi:10.48550/arxiv.1212.0622

9 pages; to appear in Archiv der Mathematik

openalex publication_date 2012/12/04 · arxiv created 2019/02/19 · arxiv updated 2019/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

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