Lectures on tensor categories and modular functors

By B. Bakalov, A. Kirillov. 2000

1,043 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b509fe444e331425d7e29dfa1aaa160d4c781c93

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Module categories, weak Hopf algebras and modular invariants (2001, methodology): “Definition 4. (see [ 1 ]) (i) Let C be a monoidal category and X be an object in”
Categorification of Skew-symmetrizable Cluster Algebras (2009, background): “For references about monoidal categories and module categories over a monoidal category, see for example [ 4 , 11, 44 ]a nd [54].”
TFT construction of RCFT correlators I: Partition functions (2002, methodology): “As already pointed out in the introduction, the framework we are going to use is the one of modular tensor categories [12,26,38, 39 ].”
Symmetry fractionalization, defects, and gauging of topological phases (2014, background): “WhenG is not a finite group, our formalism forG-crossed UBTCs described in Sec.”
Fusion categories for affine vertex algebras at admissible levels (2018, background): “The use of these lie in the fact [25, 26] that for any object N of C, the map Φ · ,N : Obj(C) → End (N) , M 7→ ΦM,N”
Differential equations and intertwining operators (2002, background): “oints are called regular in this strong sense if the system is meromorphically equivalent to a compatible (or integrable) system with singularities of logarithmic type (see, for example, Chapter 6 of [BK] for deﬁnitions of singularities of logarithmic type and regular singularities). Let G(z3) be th”
TFT construction of RCFT correlators: III: simple currents (2004, background): “[19, 20 ] as well as section I:2.4 and section 3.1 below.”
An analogue of Radford's S4 formula for finite tensor categories (2004, methodology): “Let (C, σ) be a braided finite tensor category, where σ is a natural isomorphism of bifunctors σ : ⊗ ∼ ⊗ op satisfying hexagon axioms [ BK , K]. Let Z(C) be the center”
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p(x) + ip(y) paired superfluids (2008, background): “(Here and below, for simplicity we do not explicitly write the maps lV : 1 ⊗ V → V and rV : V ⊗ 1 → V [53], which strictly should appear together with their inverses on the left hand side of this relation.”
A Finiteness Property for Braided Fusion Categories (2009, background): “The Frobenius-Perron dimension (see [8]) of a simple object FPdim(X) is defined to be the largest positive eigenvalue of the fusion matrix of X, i.e. the matrix representing X in the left regular representation of the Grothendieck semiring Gr(C) of C. Similarly, FPdim(C) is the sum of the squares…”
Anyon condensation and tensor categories (2013, background): “nditions used in some of these notions because they are usually lengthy and mysterious to the ﬁrst time readers. For more details, readers should consult with reviews of this subject (see for example [BaK][CE][M2][T][Wa]). A.1 Modular tensor categories In this subsection, we review the deﬁnition of ”
On the Classification of Topological Field Theories (2009, methodology): “Passing to the truncation τ≤1 C, we obtain a wellknown description of the free (ordinary) ribbon category on one generator in terms of framed tangles; see, for example, [3].”