6 papers
Non-semisimple link and manifold invariants for symplectic fermions
Johannes Berger, Azat M. Gainutdinov, Ingo Runkel
We consider the link and three-manifold invariants from arXiv:1912.02063, which are defined in terms of certain non-semisimple finite ribbon categories together with…
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 …
Fused K-operators and the -Onsager algebra
Guillaume Lemarthe, Pascal Baseilhac, Azat M. Gainutdinov
We study universal solutions to reflection equations with a spectral parameter, so-called K-operators, within a general framework of universal K-matrices - an extended version of t…
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…
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,…
Generalized electrical Lie algebras
Arkady Berenstein, Azat Gainutdinov, Vassily Gorbounov
We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra we associate two types (vertex t…