Rendiconti del Seminario Matematico della Università di Padova

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Volume 135, 2016, pp. 1–20
DOI: 10.4171/RSMUP/135-1

On Kaplansky’s sixth conjecture

Li Dai and Jingcheng Dong

About 39 years ago, Kaplansky conjectured that the dimension of a semisimple Hopf algebra over an algebraically closed eld of characteristic zero is divisible by the dimensions of its simple modules. Although it still remains open, some partial answers to this conjecture play an important role in classifying semisimple Hopf algebras. This paper focuses on the recent development of Kaplansky’s sixth conjecture and its applications in classifying semisimple Hopf algebras.

Keywords: Kaplansky’s sixth conjecture, semisimple Hopf algebra, fusion category, classification

Dai Li, Dong Jingcheng: On Kaplansky’s sixth conjecture. Rend. Sem. Mat. Univ. Padova 135 (2016), 1-20. doi: 10.4171/RSMUP/135-1