2024 Cluster tilting module

Cluster tilting module

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August undefined, 2024

WebDec 18, 2024 · As a main result we show that such a partial tilting module allows (up to isomorphism) at most two complements and there are two such complements if and only if the partial tilting module is ...

τ-tilting theory - preview & related info Mendeley

WebDec 29, 2007 · In [GLS2], C. Geiß, B. Leclerc and J. Schröer have shown that the module category of a preprojective algebra of Dynkin type is connected to cluster algebras in a way similar to the connection between cluster categories and cluster algebras.The preprojective algebra approach is particularly suited for cluster algebras associated to algebraic … WebJun 30, 2014 · In section 2 we have seen how the result that almost complete cluster-tilting objects in cluster categories have exactly two complements implied a similar result for … thcv leafly

Lifting to maximal rigid objects in 2-Calabi-Yau triangulated …

Webfor an almost complete tilting module, that is, a partial tilting module U satisfying U = n−1. An indecomposable module X is a complement for an almost complete tilting module U if U ⊕X is a tilting module. The following result is basic in this paper, where a Λ-module X is called faithful if the annihilator annX := {a ∈Λ aX = 0}of X ... Webcluster-tilting subcategory, then any strongly functorially nite maximal rigid subcate-gory is cluster-tilting. This result can be regarded as a simultaneous generalization of ... are equivalent to module categories under some re-striction of the functor E( ; ), see Theorem3.4and Theorem3.13for more details. ... WebThe purpose of this paper is to give an answer to Question 1.1 by investigating cluster tilting modules. Cluster tilting modules are crucial in the study of higher-dimensional … thc vista

Cluster tilting modules and noncommutative projective schemes

Webof a cluster-tilting object in C lift to cluster-tilting objects in this 2-Calabi-Yau triangulatedcategory. ThiscoincideswithFu-Liu’sresultin[FL]. Theorem 3.2. Let C be a 2-Calabi-Yau triangulated category with a cluster-tilting object T and let Γ be the endomorphism algebra of T.LetL be a tilting module over Γ;thenLlifts to a cluster ... Webtion that the module should have the same number of non-isomorphic indecomposable direct summands as the regular module. We will con- rm this conjecture by classifying … thcv mintsWebWe shall show that the stable categories of graded Cohen–Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to … thcv legality

"WebMay 30, 2024 · We then show how one can construct an n-cluster tilting subcategory for Λ by using n-fractured subcategories of A and B. As an application of our construction, we show that if n is odd and d ≥ n then there exists an algebra admitting an n-cluster tilting subcategory and having global dimension d. ... Existence of a 2-cluster tilting module ... " - Cluster tilting module

Cluster tilting module

WebDec 1, 2024 · The existence of a cluster tilting module for such an algebra A has powerful implications. It was shown by Erdmann and Holm in [11] that if A has cluster tilting … WebA finitely-generated right A-module T is called a tilting module if it has the following three properties: T has projective dimension at most 1, in other words it is a quotient of a …

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WebIt is an open question whether all -cluster tilting subcategories are given by -cluster tilting modules. Nevertheless, if we assume the existence of a -cluster tilting module we can obtain further results about C add . In particular in this case Cis directed if and only if add is directed. Furthermore it is asked in [10]ifthemere existence of a ... WebJan 27, 2024 · Non-singular weighted surface algebras satisfy the necessary condition found in [6] for existence of cluster tilting modules. We show that any such algebra whose Gabriel quiver is bipartite, has a module satisfying the necessary ext vanishing condition. We show that it is 3-cluster tilting precisely for the non-singular triangular or spherical …

WebOct 24, 2024 · We show that for every X in C_w, \vphi_X coincides after appropriate changes of variables with the cluster characters of Fu and Keller associated with any cluster-tilting module T of C_w. WebJan 1, 2024 · Let G = S L (2, 5) be the special linear group of 2 × 2-matrices with coefficients in the field with 5 elements.We show that the principal block over a splitting field K of …

WebNov 11, 2024 · Let C be an (n+2)-angulated category with an n-suspension functor Σ ⁿ and X be a cluster-tilting subcategory of C. Then we show that the quotient category C/X is an n-abelian category, and C/X ... WebAn important property in cluster-tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly two cluster-tilting objects. ... and show that an almost complete support $\tau $-tilting module has exactly two complements for any finite-dimensional algebra. For a finite-dimensional ...

Web0, we can see this as a generalised tilting module. Thus Rickard’s question can be specialised to generalised tilting modules. In higher dimensional Auslander-Reiten theory, rst introduced by Iyama in [8], one studies d-cluster tilting subcategories instead of the whole module-category.

WebIntroduction Tilting Cluster-tilting ˝-tiltingBibliography Setup isaﬁnite-dimensionalalgebraover k= . mod isthecategoryofﬁnitelygeneratedleft -modules. proj … thc vofWebTheorem 1 (6). Any partial tilting module is a direct summand of a tilting module. It is natural to ask how many tilting modules exist for a given partial tilting module. There is … thcv moleculeWebNov 23, 2007 · The study of their tilting modules is a step in this direction. In [19], a tilting module over a cluster-tilted algebra has been proved to lift to a cluster-tilting object in … thcv ocsWebTheorem. There exists a connected algebra Athat admits a 2-cluster tilting module and a simple A-module Swhich has in nite complexity. 1. An algebra with a 2-cluster tilting … thcv near meWebOct 12, 2024 · Given $n\leq d<\infty $, we investigate the existence of algebras of global dimension d which admit an n-cluster tilting subcategory.We construct many such examples using representation-directed algebras. First, given two representation-directed algebras A and B, a projective A-module P and an injective B-module I satisfying … thcv meaningWebJul 19, 2024 · Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2-Calabi-Yau triangulated category ℬ , a functorially finite, extension closed subcategory 𝒯 of ℬ is cluster tilting if and only if ℬ /𝒯 is an ... thcv melting pointWebThe 1-cluster tilting module A1 n Mis an additive generator of the whole module category modA1 n. So the d D1 case of the previous result is the fact that the non-projective-injective indecomposable modules of A1 ncan be identiﬁed with the diagonals of an .nC2/-gon in such a way that tilting modules for A1 thc vomiting