Related papers: Mittag Leffler modules and definable subcategories
A careful exposition of Zilber's quasiminimal excellent classes and their categoricity is given, leading to two new results: the L_w1,w(Q)-definability assumption may be dropped, and each class is determined by its model of dimension…
We classify integrable irreducible $\hat{g}[\sigma]$-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modules and their tensor product modules.
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.
The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of groups where finite generation is not assumed. We also…
We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore,…
Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of this category and thereby extend a result of Leuschke to the…
In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.
We obtain a classification of metaplectic modular categories: every metaplectic modular category is a gauging of the particle-hole symmetry of a cyclic modular category. Our classification suggests a conjecture that every weakly-integral…
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and…
We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
In this paper we study the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$, the category of integrable level-$k$ respresentations of affine Kac-Moody $\mathfrak{sl}_N$. Our first main result classifies these module…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in…
In this paper we propose unifying the categories of cochain complexes $\text{Ch}(\mathcal{C})$ and modules $\widehat{A}\text{-mod}$ over a repetitive algebra $\widehat{A}$. Motivated by their striking similarities and importance, we…
In this paper we study the subcategory of cuspidal modules of the category of weight modules over the Lie algebra sl(n+1). Our main result is a complete classification and explicit description of the indecomposable cuspidal modules.
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point…
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for…