90 citations · 865 across the 43 of their papers we have counts for
49 papers
Cellular Algebra of webs
Azat M. Gainutdinov, Jesper Lykke Jacobsen, Yueheng Li
We introduce a diagram algebra based on Kuperberg's -webs and prove a Schur--Weyl duality $\mathcal{K}_L \cong \operatorname{End}_{U_q(\mathfrak{sl}_3)}((V^+ \…
Crossed-module crossed braided categories
Azat M. Gainutdinov, Ingo Runkel, Bangxin Wang
For a crossed module , we introduce the notion of -crossed braided (resp. ribbon) categories, where the categories are graded by group and carry an -action. O…
Deformations of mixed associators in module categories
Matthieu Faitg, Azat M. Gainutdinov, Christoph Schweigert +1
We set up a cochain complex whose cohomology controls deformations of the mixed associator of a module category over a …
Fully exact and fully dualizable module categories
Azat M. Gainutdinov, Robert Laugwitz
We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast,…
Universal TT- and TQ-relations via centrally extended q-Onsager algebra
Pascal Baseilhac, Azat M. Gainutdinov, Guillaume Lemarthe
Let be the alternating central extension of the q-Onsager algebra, a comodule algebra over the quantum loop algebra of . We classify one-dimensional representations of…
An adjunction theorem for Davydov-Yetter cohomology and infinitesimal braidings
Matthieu Faitg, Azat M. Gainutdinov, Christoph Schweigert
Davydov-Yetter cohomology is associated to a monoidal functor between -linear monoidal categories where $\Bbb…