Related papers: Bijections between $\tau$-rigid modules

We relate general maps to bipartite maps through a bijection of type slit-slide-sew. We provide an involution on arbitrary genus maps with even degree faces. This enables a full interpretation of the relation between general and bipartite…

We present an elementary type preserving bijection between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis.

For finite-dimensional algebras over algebraically closed fields, we consider two fundamental classes of modules and their geometric counterparts: bricks and $\tau$-rigid modules, as well as brick components and $\tau$-regular components.…

Let ${p > 2}$ be an odd prime and ${G = SL_2(\mathbb{F}_p)}$. Denote the subgroup of upper triangular matrices as $B$. Finally, let ${\mathbb{F}}$ be an algebraically closed field of characteristic ${p}$. The Green correspondence gives a…

We give a geometric model for the non-$\tau$-rigid modules over acyclic path algebras of type $\widetilde{D}_n$. Similar models have been provided for module categories over path algebras of types $A_n, D_n,$ and $\widetilde{A}_n$ as well…

This paper is devoted to derivations in bimodules over group rings using previously proposed methods which are related to character spaces over groupoids. The theorem describing the arising spaces of derivations is proved. We consider some…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the…

Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have…

We show that indecomposable two-term presilting complexes over $\Pi_{n}$, the preprojective algebra of $A_{n}$, are in bijection with internal $n$-simplices in the prism $\Delta_{n} \times \Delta_{1}$, the product of an $n$-simplex with a…

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…

There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the…

We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes…

In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…

Let $\Lambda$ be an Artin algebra and $K^b(proj(\Lambda))$ be the triangulated category of bounded co-chain complexes in $proj(\Lambda).$ It is well known that two-terms silting complexes in $K^b(proj(\Lambda))$ are described by the…

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.

Let $\mathscr T$ be a $2$-Calabi--Yau triangulated category, $T$ a cluster tilting object with endomorphism algebra $\Gamma$. Consider the functor $\mathscr T( T,- ) : \mathscr T \rightarrow \mod \Gamma$. It induces a bijection from the…

We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form $(B^{2,1})^{\otimes L}$ in the $G_{2}^{(1)}$ adjoint crystals.

This work proves that the process of gluing finite lattices to form a larger lattice is bijective, that is each lattice is the glued sum of a unique system of finite lattices, provided the class of lattices is constrained to modular,…

We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting…