Reductions of Tensor Categories Modulo Primes

Autor:	Pavel Etingof, Shlomo Gelaki
Přispěvatelé:	Massachusetts Institute of Technology. Department of Mathematics, Etingof, Pavel I.
Rok vydání:	2011
Předmět:	Pure mathematics Algebra and Number Theory Almost prime Mathematics::Number Theory Modulo Good prime Prime number Safe prime Mathematics::Category Theory Mathematics - Quantum Algebra Converse FOS: Mathematics Unique prime Quantum Algebra (math.QA) Permutable prime Mathematics
Zdroj:	arXiv
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927872.2011.617267
Popis:	Original manuscript February 12, 2011 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. National Science Foundation (U.S.) (Grant DMS-1000113) United States-Israel Binational Science Foundation (Grant 2008164)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aecef35d9eab45c347680f5329435d0f https://doi.org/10.1080/00927872.2011.617267 Zobrazit plný text záznamu