On braided fusion categories I

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.

102 pages, LaTeX, typos corrected

References in corpus (3)

• Homotopy field theory in dimension 3 and crossed group-categories
• The notion of category over an algebraic stack
• Weakly group-theoretical and solvable fusion categories

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