Related papers: Balanced pairs and tilting modules in recollement

Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…

We relate the combinatorics of Hall-Littlewood polynomials to that of abelian $p$-groups with alternating or Hermitian perfect pairings. Our main result is an analogue of the classical relationship between the Hall algebra of abelian…

Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.

From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\mathcal{X} , \omega ); (\nu, \mathcal{Y})]$ as a tool to induce balanced pairs $(\mathcal{X} , \mathcal{Y} )$ for the…

We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the equivalences induced by a finitely generated tilting module over artin algebras, to the case of an infinitely generated tilting module over an arbitrary…

We introduce a class of orders on $P^d$ called Geigle-Lenzing orders and show that they have tilting bundles. Moreover we show that their module categories are equivalent to the categories of coherent sheaves on Geigle-Lenzing spaces…

We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective…

These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…

This is a review (including some background material) of the author's work and related activity on certain exactly solvable statistical models in two dimensions, including the six-vertex model, loop models and lozenge tilings. Applications…

We study a structure of subcategories which are called a polygon of recollements in a triangulated category. First, we study a $2n$-gon of recollements in an $(m/n)$-Calabi-Yau triangulated category. Second, we show the homotopy category…

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated to a triangle functor from the category on the right to the category on the left. For a morphic…

For a triangulated category T, if C is a cluster-tilting subcategory of T, then the quotient category T\C is an abelian category. Under certain conditions, the converse also holds. This is an very important result of cluster-tilting theory,…

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories:…

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…

It is natural to study octonion Hilbert spaces as the recently swift development of the theory of quaternion Hilbert spaces. In order to do this, it is important to study first its algebraic structure, namely, octonion modules. In this…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent…

In the paper we first construct a new cotorsion pair, in the category of chain complexes, from two given cotorsion pairs in the category of modules, and then we consider completeness of such pairs under certain conditions.