Related papers: Almost split sequences for Knorr lattices

Let $A$ be a truncated polynomial ring over a complete discrete valuation ring $\mathcal{O}$, and we consider the additive category consisting of $A$-lattices $M$ with the property that $M\otimes \mathcal{K}$ is projective as an $A\otimes…

This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…

Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence…

An $m \times n$ matrix $\mathsf{A}$ with column supports $\{S_i\}$ is $k$-separable if the disjunctions $\bigcup_{i \in \mathcal{K}} S_i$ are all distinct over all sets $\mathcal{K}$ of cardinality $k$. While a simple counting bound shows…

We consider the Kronecker algebra $A=\mathcal{O}[X, Y]/(X^2, Y^2)$, where $\mathcal{O}$ is a complete discrete valuation ring. Since $A \otimes\kappa$ is a special biserial algebra, where $\kappa$ is the residue field of $\mathcal{O}$, one…

A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterisation is used to study simple R-modules in terms of their Ext groups. It is…

The category of quasi frames (or qframes) is introduced and studied. In the context of qframes we can jointly study problems related to the L-Surjunctivity and Stable Finiteness Conjectures. As a consequences of our main results, we can…

For a finite lattice L, let EL denote the reflexive and transitive closure of the join-dependency relation on L, defined on the set J(L) of all join-irreducible elements of L. We characterize the relations of the form EL, as follows:…

Let $\mathcal{O}$ be a complete discrete valuation ring, $\mathcal{K}$ its quotient field, and $A$ the symmetric Kronecker algebra over $\mathcal{O}$. We consider the full subcategory of the category of $A$-lattices whose objects are…

We study the behaviour of almost split sequences and \art quivers of an order under rejection of bijective modules. In particular, we establish relations of stable categories and almost split sequences for an order $A$ and the order $A'$…

Let k be a field, Q a quiver with countably many vertices and I an ideal of kQ such that kQ/I has finite dimensional Hom-spaces. In this note, we prove that there is no almost split sequence ending at an indecomposable not finitely…

We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…

We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that…

Let $J$ be an almost complex structure on a 4-dimensional and unimodular Lie algebra $\mathfrak{g}$. We show that there exists a symplectic form taming $J$ if and only if there is a symplectic form compatible with $J$. We also introduce…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

We develop a general theory of local stability up to belonging to an ideal (e.g. having measure zero). From a model-theoretic perspective, we prove a stationarity principle for almost stable formulas in this sense, and build a topological…

Almost split sequences lie in the heart of Auslander-Reiten theory. This paper deals with the structure of almost split sequences with certain ending terms in the morphism category of an Artin algebra $\Lambda$. Firstly we try to interpret…