相关论文: Braid action on derived category of Nakayama algeb…
In the paper, we prove that there exists a braid group action on the extended crystal $\widehat{B}(\infty)$ of finite type. The extended crystal $\widehat{B}(\infty)$ and its braid group action are investigated from the viewpoint of crystal…
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
We construct a braid group action on a homotopy category of $p$-DG modules of a deformed Webster algebra.
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the…
We construct an action of the braid group on the bounded derived category of coherent sheaves on hypertoric varieties arising from hyperplane arrangements. Using wall-crossing equivalences associated to paths in the complexified complement…
In this paper, we study Azumaya algebras and Brauer groups in derived algebraic geometry. We establish various fundamental facts about Brauer groups in this setting, and we provide a computational tool, which we use to compute the Brauer…
This is the first of two papers on quasi-split affine quantum symmetric pairs $\big(\widetilde{\mathbf U}(\widehat{\mathfrak g}), \widetilde{{\mathbf U}}^\imath \big)$, focusing on the real rank one case, i.e., $\mathfrak{g}=…
In our proceeding paper a generating set of the derived Picard group of a selfinjective Nakayama algebra was constructed combining some previous results for Brauer tree algebras and the technique of orbit categories developed there. In this…
This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley-Lieb categories. If $\mathcal K$ denotes any of these categories, and if $\sigma\in\mathcal K_{nm}$ is…
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect derived category $\mathsf{K^b(A)}$ of a gentle algebra $\mathsf{A}$. We show that full…
We demonstrate that the blocks of a profinite group whose defect groups are cyclic have a Brauer tree algebra structure analogous to the case of finite groups. We show further that the Brauer tree of a block with defect group…
We introduce a new algebra called the shifted $q=0$ affine algebra, which arises naturally from the study of coherent sheaves on Grassmannians and n-step partial flag varieties via a natural correspondence. It has similar presentation as…
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…
Let $(\bar{M}, \omega)$ be a compact symplectic manifold with convex boundary and $c_1(T\bar{M})=0$. Suppose that $(\bar{M}, \omega)$ is equipped with a convex Hamiltonian $G$-action for some connected, compact Lie group $G$. We construct…
An associative central simple algebra is a form of matrices, because a maximal \'{e}tale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of…
Let $A$ be a ring equipped with a derivation $\delta $. We study differential Azumaya $A$ algebras, that is, Azumaya $A$ algebras equipped with a derivation that extends $\delta $. We calculate the differential automorphism group of the…
We construct a p-DG structure on an algebra Koszul dual to a zigzag algebra used by Khovanov and Seidel to construct a categorical braid group action. We show there is a braid group action in this p-DG setting.
Recently, Chang--Haiden--Schroll shows that the braid group action on full exceptional collections in a triangulated category is not transitive but has infinitely many orbits in general. Their proof is based on a geometric model and the…
We shed some light on the problem of determining the orbits of the braid group action on semiorthonormal bases of Mukai lattices as considered in \cite{GK04} and \cite{GO1}. We show that there is an algebraic (and in particular algorithmic)…
We prove that the quantum toroidal algebras $\mathcal{E}_\mathbf{s}$ associated with different root systems $\mathbf{s}$ of $\mathfrak{gl}_{m|n}$ type are isomorphic. We also show the existence of Miki automorphism of…