On braided fusion categories I

Authors:
  • VDVladimir Drinfeld
    Vladimir Drinfeld
  • SGShlomo Gelaki
    Shlomo Gelaki
  • DNDmitri Nikshych
    Dmitri Nikshych
  • VOVictor Ostrik
    Victor Ostrik
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Abstract
This work is a detailed version of arXiv:0704.0195 [math.QA]. We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also give a comprehensive and self-contained exposition of the known results on braided fusion categories without assuming them pre-modular or non-degenerate. The guiding heuristic principle of our work is an analogy between braided fusion categories and Casimir Lie algebras.