相关论文: Simple transitive $2$-representations of left cell…

We show that every simple transitive $2$-representation of the $2$-category of projective functors for a certain quotient of the quadratic dual of the preprojective algebra associated with a tree is equivalent to a cell $2$-representation.

We classify simple transitive $2$-representations of certain $2$-sub\-ca\-te\-go\-ri\-es of the $2$-category of Soergel bimodules over the coinvariant algebra in Coxeter types $B_2$ and $I_2(5)$. In the $I_2(5)$ case it turns out that…

We show that any simple transitive $2$-representation of the $2$-ca\-te\-go\-ry of projective endofunctors for the quiver algebra of $\Bbbk(\xymatrix{\bullet\ar[r]&\bullet})$ and for the quiver algebra of…

We prove that every simple transitive $2$-representation of the fiat $2$-category of Soergel bimodules (over the coinvariant algebra) in type $B_2$ is equivalent to a cell $2$-representation. We also describe some general properties of the…

We classify all simple transitive $2$-representations for two classes of finitary $2$-categories associated with tree path algebras and also for one class of fiat $2$-categories associated with truncated polynomial rings. Additionally, we…

In this article, we define and study the class of simple transitive $2$-representations of finitary $2$-categories. We prove a weak version of the classical Jordan-H\"older Theorem where the weak composition subquotients are given by simple…

Given a finite dimensional algebra $A$, we consider certain sets of idempotents of $A$, called self-injective cores, to which we associate 2-subcategories of the 2-category of projective bimodules over $A$. We classify the simple transitive…

In all finite Coxeter types but $I_2(12)$, $I_2(18)$ and $I_2(30)$, we classify simple transitive $2$-rep\-re\-sen\-ta\-ti\-ons for the quotient of the $2$-category of Soergel bimodules over the coinvariant algebra which is associated to…

We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations…

We study the classification problem of simple transitive 2-representations of the 2-category of finite-dimensional bimodules over a radical square zero Nakayama algebra. This results in a complete classification of simple transitive…

We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank…

The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive $2$-representations with a fixed apex $\mathcal{J}$ of a fiat $2$-category $\cC$ and the set of equivalence classes of…

We determine for which Coxeter types the associated small quotient of the $2$-category of Soergel bimodules is finitary and, for such a small quotient, classify the simple transitive $2$-representations (sometimes under the additional…

In this paper we complete the $\mathrm{ADE}$-like classification of simple transitive $2$-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag…

In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple…

For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms…

We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive…

Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…

We introduce the class of isotypic $2$-representations for finitary $2$-categories and the notion of inflation of $2$-representations. Under some natural assumptions we show that isotypic $2$-representations are equivalent to inflations of…

In this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive $2$-representations and we complete their classification in all types but $H_{3}$ and $H_{4}$.