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pro vyhledávání: '"Davydov, Alexei"'
Autor:
Davydov, Alexei
Publikováno v:
Encyclopedia of Mathematical Physics 2nd edition,2024, Chapter 50007
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
Externí odkaz:
http://arxiv.org/abs/2311.05789
Autor:
Davydov, Alexei, Nikshych, Dmitri
We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to braided monoida
Externí odkaz:
http://arxiv.org/abs/2006.08022
Autor:
Batanin, Michael, Davydov, Alexei
We introduce a notion of $n$-commutativity ($0\le n\le \infty$) for cosimplicial monoids in a symmetric monoidal category ${\bf V}$, where $n=0$ corresponds to just cosimplicial monoids in ${\bf V,}$ while $n=\infty$ corresponds to commutative cosimp
Externí odkaz:
http://arxiv.org/abs/2003.13039
Autor:
Davydov, Alexei, Elbehiry, Mohamed
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 object (the so-called Schur-Weyl categories). Using this description we
Externí odkaz:
http://arxiv.org/abs/1908.09192
Autor:
Bischoff, Marcel, Davydov, Alexei
Publikováno v:
Transformation Groups. 2020
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 allows us to see the algebra as the regular algebra in the representation
Externí odkaz:
http://arxiv.org/abs/1811.10528
Autor:
Davydov, Alexei, Simmons, Darren
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 category of $G$), which is isomorphic to the third
Externí odkaz:
http://arxiv.org/abs/1704.02401
We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group $\mathfrak{u}_q(\mathfrak{g})$, where $q$ is a root of unity.
Comment: 29 pages, latex
Comment: 29 pages, latex
Externí odkaz:
http://arxiv.org/abs/1703.06543
Publikováno v:
In Transportation Research Procedia 2022 61:333-339
Autor:
Davydov, Alexei, Simmons, Darren
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 module categories over pointed fusion categories.
Externí odkaz:
http://arxiv.org/abs/1603.04650