Lectures on tensor categories and modular functors

@inproceedings{Bakalov2000LecturesOT,
  title={Lectures on tensor categories and modular functors},
  author={Bojko Bakalov and Alexander A. Kirillov},
  year={2000}
}
Introduction Braided tensor categories Ribbon categories Modular tensor categories 3-dimensional topological quantum field theory Modular functor Moduli spaces and complex modular functor Wess-Zumino-Witten model Bibliography Index Index of notation. 
Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper
The rank of 𝐺-crossed braided extensions of modular tensor categories
We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.
CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY
We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first
GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY
We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16, 19] by a certain fractional power of the abelian theory first
On Certain Integral Tensor Categories and Integral TQFTs
We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over some ring of algebraic integers. We show how to obtain TQFTs
Modular categories as representations of the 3-dimensional bordism 2-category
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories
Duality Theorem and Hom Functor in Braided Tensor Categories
Blatter-Montgomery duality theorem is generalized into braided tensor categories. It is shown that $Hom(V,W)$ is a braided Yetter-Drinfeld module for any two braided Yetter-Drinfeld modules $V$ and
Conformal field theory, tensor categories and operator algebras
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized.
Quantization of moduli spaces of flat connections and Liouville theory
We review known results on the relations between conformal field theory, the quantization of moduli spaces of flat PSL(2,R)-connections on Riemann surfaces, and the quantum Teichmueller theory.
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