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Reductions of Tensor Categories Modulo Primes

Author(s)
Gelaki, Shlomo; Etingof, Pavel I.
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Abstract
We study good (i.e., semisimple) reductions of semisimple rigid tensor categories modulo primes. A prime p is called good for a semisimple rigid tensor category C if such a reduction exists (otherwise, it is called bad). It is clear that a good prime must be relatively prime to the Müger squared norm |V|[superscript 2] of any simple object V of C. We show, using the Ito–Michler theorem in finite group theory, that for group-theoretical fusion categories, the converse is true. While the converse is false for general fusion categories, we obtain results about good and bad primes for many known fusion categories (e.g., for Verlinde categories). We also state some questions and conjectures regarding good and bad primes.
Description
Original manuscript February 12, 2011
Date issued
2011-12
URI
http://hdl.handle.net/1721.1/80866
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Communications in Algebra
Publisher
Taylor & Francis
Citation
Etingof, Pavel, and Shlomo Gelaki. “Reductions of Tensor Categories Modulo Primes.” Communications in Algebra 39, no. 12 (December 2011): 4634-4643.
Version: Original manuscript
ISSN
0092-7872
1532-4125

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