On Lagrangian algebras in group-theoretical braided fusion categories

  title={On Lagrangian algebras in group-theoretical braided fusion categories},
  author={Alexei Davydov and Darren Simmons},
  journal={arXiv: Quantum Algebra},

Computing the Group of Minimal Non-degenerate Extensions of a Super-Tannakian Category

  • D. Nikshych
  • Mathematics
    Communications in Mathematical Physics
  • 2022
We prove an analog of the Künneth formula for the groups of minimal non-degenerate extensions (Lan et al. in Commun Math Phys 351:709–739, 2017) of symmetric fusion categories. We describe in detail

Reconstruction and local extensions for twisted group doubles, and permutation orbifolds

We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation

Third Cohomology and Fusion Categories

It was observed recently that for a fixed finite group $G$, the set of all Drinfeld centres of $G$ twisted by 3-cocycles form a group, the so-called group of modular extensions (of the representation

Braid group representations from braiding gapped boundaries of Dijkgraaf–Witten theories

We study representations of the braid groups from braiding gapped boundaries of Dijkgraaf-Witten theories and their twisted generalizations, which are (twisted) quantum doubled topological orders in

Conformal Net Realizability of Tambara-Yamagami Categories and Generalized Metaplectic Modular Categories

We show that all isomorphism classes of even rank Tambara-Yamagami categories arise as $\mathbb{Z}_2$-twisted representations of conformal nets. As a consequence, we show that their Drinfel'd centers

On Lagrangian Algebras in Braided Fusion Categories



The Witt group of non-degenerate braided fusion categories

Abstract We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid

Centre of an algebra

Module categories over the Drinfeld double of a finite group

. We classify the module categories over the double (possibly twisted) of a finite group.

Algebraic Aspects of Orbifold Models

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly.

On braided fusion categories I

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

Module categories, weak Hopf algebras and modular invariants

AbstractWe develop a theory of module categories over monoidal categories (this is a straightforward categorization of modules over rings). As applications we show that any semisimple monoidal

Modular invariants for group-theoretical modular data. I

Correspondences of ribbon categories

  • Fr
  • Mathematics
  • 2003
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories.

Homotopy field theory in dimension 2 and group-algebras

We apply the idea of a topological quantum field theory (TQFT) to maps from manifolds into topological spaces. This leads to a notion of a (d+1)-dimensional homotopy quantum field theory (HQFT) which

Finite group modular data