Related papers: Drinfeld centralizers and Rouquier complexes

We consider categories of Soergel bimodules for the symmetric groups S_n in their gl(n)-realizations for all n and assemble them into a locally linear monoidal bicategory. Chain complexes of Soergel bimodules likewise form a locally…

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

Let $\ca$ be a small dg category over a field $k$ and let $\cu$ be a small full subcategory of the derived category $\cd\ca$ which generate all free dg $\ca$-modules. Let $(\cb,X)$ be a standard lift of $\cu$. We show that there is a…

We prove the existence of an $m$-cluster tilting object in a generalized $m$-cluster category which is $(m+1)$-Calabi-Yau and Hom-finite, arising from an $(m+2)$-Calabi-Yau dg algebra. This is a generalization of the result for the ${m =…

The Drinfeld twists or factorizing F-matrices for the open XXZ spin chain with non-diagonal boundary terms are constructed. It is shown that in the F-basis the two sets of pseudo-particle creation operators simultaneously take completely…

In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of…

Let $(\mathcal{X}, \mathcal{Y})$ be a balanced pair in an abelian category $\mathcal{A}$. Denote by ${\bf K}_{\mathcal{E}\text{-}{\rm ac}}(\mathcal{X})$ the chain homotopy category of right $\mathcal{X}$-acyclic complexes with all items in…

We introduce the notion of Drinfeld modular forms with $A$-expansions, where instead of the usual Fourier expansion in $t^n$ ($t$ being the uniformizer at `infinity'), parametrized by $n \in \mathbb{N}$, we look at expansions in $t_a$,…

Let $\mathcal{M}$ be an $n$-cluster tilting subcategory of ${\rm mod}\mbox{-}\Lambda$, where $\Lambda$ is an artin algebra. Let $\mathcal{S}(\mathcal{M})$ denotes the full subcategory of $\mathcal{S}(\Lambda)$, the submodule category of…

Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…

We prove that the notion of Drinfeld center defines a functor from the category of indecomposable multi-tensor categories with morphisms given by bimodules to that of braided tensor categories with morphisms given by monoidal bimodules.…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

In this paper, we introduce the notion of a four-angle Hopf module for a Hom-Hopf algebra $(H,\beta)$ and show that the category $\!^{H}_{H}\mathfrak{M}^{H}_{H}$ of four-angle Hopf modules is a monoidal category with either a Hom-tensor…

In this article, we present actions by central elements on Hochschild cohomology groups with arbitrary bimodule coefficients, as well as an interpretation of these actions in terms of exact sequences. Since our construction utilises the…

Let ${\mathcal X}$ be a category fibered in groupoids over a finite field $\mathbb{F}_q$, and let $k$ be an algebraically closed field containing $\mathbb{F}_q$. Denote by $\phi_k\colon {\mathcal X}_k\to {\mathcal X}_k$ the arithmetic…

The monomorphism category $\mathscr{S}(A, M, B)$ induced by a bimodule $_AM_B$ is the subcategory of $\Lambda$-mod consisting of $\left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_{\phi}$ such that $\phi: M\otimes_B Y\rightarrow X$ is…

Given a Hopf algebra $H$ and a counital $2$-cocycle $\mu$ on $H$, Drinfeld introduced a notion of twist which deforms an $H$-module algebra $A$ into a new algebra $A_\mu$. We show that when $A$ is a quadratic algebra, and $H$ acts on $A$ by…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

Let $F$ be a function field over $\mathbb{F}_q$, $A$ its ring of regular functions outside a place $\infty$ and $\mathfrak{p}$ a prime ideal of $A$. First, we develop Hida theory for Drinfeld modular forms of rank $r$ which are of slope…

Building on Retakh's approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras both from splicing extensions (leading to…