Related papers: Hook-decomposable modules and their resolutions

We study the decomposability of Specht modules labelled by bihooks, bipartitions with a hook in each component, for the Iwahori--Hecke algebra of type $B$. In all characteristics, we determine a large family of decomposable Specht modules,…

The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described entirely by the barcode invariant. In this paper we…

A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…

We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main…

In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered…

Let $L/K$ be a finite Galois extension of fields with group $\Gamma$. Associated to each Hopf-Galois structure on $L/K$ is a group $G$ of the same order as the Galois group $\Gamma$. The type of the Hopf-Galois structure is by definition…

Algebraic persistence studies persistence modules (typically, linear representations of the poset $\mathbf{R}^n$ with $n \geq 1$) and the algebraic relationships between persistence modules that are interleaved. The notion of…

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…

We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology…

Multiparameter persistence modules come up naturally in topological data analysis and topological robotics. Given a metric graph $(X,\delta)$, the second configuration space of $(X,\delta)$ with proximity parameters (for example, the…

Persistence modules stratify their underlying parameter space, a quality that make persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter…

We consider the homotopy category of complexes of projective modules over any gentle algebra. We prove that indecomposable $\Sigma$-pure-injective objects in s must be shifts of string or band complexes. We begin with a survey of purity in…

We prove the decomposition theorem for Hodge modules with integral structure along proper K\"ahler morphisms, partially generalizing M. Saito's theorem for projective morphisms. Our proof relies on compactifications of period maps of…

Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori--Hecke algebra of type $B$. In most cases we conjectured that these were the only decomposable Specht modules…

Let $F,G$ be bicomonads on a monoidal category $\mathcal{C}$. The aim of this paper is to discuss the smash coproducts of $F$ and $G$. As an application, the smash coproduct of Hom-bialgebras is discussed. Further, the Hom-entwining…

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

In Part 1, we describe six projective-type model structures on the category of differential graded modules over a differential graded algebra A over a commutative ring R. When R is a field, the six collapse to three and are well-known, at…

In this paper, we introduce the notion of a BCK-topological module in a natural way and establish that every decreasing sequence of submodules on a BCK-module M over bounded commutative BCK-algebra X is indeed a BCK- topological module. We…

In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…