49 citations · 159 across the 23 of their papers we have counts for
18 papers · 1 filter
Braided Picard groups and graded extensions of braided tensor categories
Alexei Davydov, Dmitri Nikshych
We classify various types of graded extensions of a finite braided tensor category in terms of its -categorical Picard groups. In particular, we prove that braided exte…
Deformation cohomology of Schur-Weyl categories. Free symmetric categories
Alexei Davydov, Mohamed Elbehiry
The deformation cohomology of a tensor category controls deformations of its monoidal structure. Here we describe the deformation cohomology of tensor categories generated by one o…
Hopf algebra actions in tensor categories
Marcel Bischoff, Alexei Davydov
We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action all…
Autoequivalences of tensor categories attached to quantum groups at roots of
Alexei Davydov, Pavel Etingof, Dmitri Nikshych
We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group , where…
On Lagrangian algebras in group-theoretical braided fusion categories
Alexei Davydov, Darren Simmons
We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and…
Holomorphic Symplectic Fermions
Alexei Davydov, Ingo Runkel
Let V be the even part of the vertex operator super-algebra of r pairs of symplectic fermions. Up to two conjectures, we show that V admits a unique holomorphic extension if r is a…