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Frobenius-Perron Dimensions of Integral \(\mathbb {Z}_{+}\)-rings and Applications

  • Pavel EtingofEmail author
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Abstract

We introduce the notion of the Frobenius-Perron dimension of an integral \(\mathbb {Z}_{+}\)-ring and give some applications of this notion to classification of finite dimensional quasi-Hopf algebras with a unique nontrivial simple module, and of quasi-Hopf and Hopf algebras of prime dimension p.

Keywords

Hopf algebra quasi-Hopf algebra Frobenius-Perron dimension 

Mathematics Subject Classification (2010)

16T05 18D10 

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Notes

Acknowledgements

The author is grateful to C. Negron for useful discussions and to V. Ostrik, S.-H. Ng and X. Wang for corrections and comments on the draft of this paper. The work of the author was partially supported by the NSF grant DMS-1502244.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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