相关论文: The dual actions, equivariant autoequivalences and…

Consider a finite group $G$ acting on a triangulated category $\mathcal T$. In this paper we investigate triangulated structure on the category $\mathcal T^G$ of $G$-equivariant objects in $\mathcal T$. We prove (under some technical…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

For an abelian category with a Serre duality and a finite group action, we compute explicitly the Serre duality on the category of equivariant objects. Special cases and examples are discussed. In particular, an abelian category with a…

We formulate a version of Beck's monadicity theorem for abelian categories, which is applied to the equivariantization of abelian categories with respect to a finite group action. We prove that the equivariantization is compatible with the…

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…

The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…

We prove that the categories of coherent sheaves over weighted projective lines of tubular type are explicitly related to each other via the equivariantization with respect to certain cyclic group actions.

This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

We investigate group actions on the category of coherent sheaves over weighted projective lines. We show that the equivariant category with respect to certain finite group action is equivalent to the category of coherent sheaves over a…

We introduce a new invariant of $G$-varieties, the dual complex, which roughly measures how divisors in the complement of the free locus intersect. We show that the top homology group of this complex is an equivariant birational invariant…

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not…

The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular…

We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences \`a la Pronk, localising using surjective submersive equivariant…

We study group action on bimodules and bimodule categories and prove for them analogues of the results known for representations of skew group algebras, mainly in the case, when the action is separable.

The string group acts on the category of coherent sheaves over a weighted projective line by degree-shift actions. We study the equivariant equivalence relations induced by degree-shift actions between weighted projective lines. We prove…

Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We introduce a notion of equivariant $\mathcal{D}$-stability for actions of unitary tensor categories on C$^*$-algebras. We show that, when $\mathcal{D}$ is strongly self-absorbing, equivariant $\mathcal{D}$-stability of an action is…