On braided fusion categories I

By V. Drinfeld, Shlomo Gelaki, D. Nikshych, V. Ostrik. 2009

463 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a86fac6531b60080a2d729c60fd3ec8d35c9c84

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Anyons and matrix product operator algebras (2015, background): “the gapped topological orders that can be realized on the boundary of a two-dimensional bulk [34].”
Centers of graded fusion categories (2009, methodology): “It was explained in [Müger 2000; Drinfeld et al. 2009] that the group G acts on CG by tensor autoequivalences (this action comes from the action of G on A by right translations).”
The Picard crossed module of a braided tensor category (2012, background): “ensor categories. In particular, they are used in the classiﬁcation of group extensions of fusion categories [ENO]. They also appear as parts of an important invariant of C called the core studied in [DGNO]. We thus hope that our description of the algebraic structure formed by these groups will she”
On dualizability of braided tensor categories (2018, background): “over k, an A-algebra can be deﬁned either as an algebra object in the monoidal category A-mod, or equivalently as a k-algebra Btogether with an algebra morphism A−→ Z(B). This motivates the following [DGNO10]: Deﬁnition-Proposition 3.2. Given a braided tensor category A, the following two notions ar”
Cyclotomic Integers, Fusion Categories, and Subfactors (2010, unknown): “We refer the reader to [13, 11] for a general theory of fusion and braided fusion categories.”
Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model (2013, background): “[39] Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik.”