2024 Cluster tilting module

Cluster tilting module

Author: dplh

August undefined, 2024

WebWe 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 … WebFurthermore, if C=EndAT for a tilting module T over a hereditary algebra A, we compare the induction and coinduction functors to the Buan-Marsh-Reiten functor HomCA (T,−) from the cluster-category of A to the module category of B. We also study the question as to which B-modules are actually induced or coinduced from a module over a tilted ...

Induced and coinduced modules over cluster-tilted algebras

WebTheorem. 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 … 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 ... slang word for romani people

Max-Planck-Institut für Mathematik Bonn

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 … 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. Reformulated for path algebras kQ, this says that an almost complete support tilting module has exactly two complements. 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. slang word for sandwich

Gluing of n-Cluster Tilting Subcategories for Representation-directed ...

Tilting modules in d-cluster tilting subcategories - DiVA portal

WebThe 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 WebJul 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 ... slang word for thickWebTheorem 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 … slang word for tea

"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 … " - Cluster tilting module

Cluster tilting module

WebNov 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 … 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 …

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WebJan 3, 2024 · We describe what it means for an algebra to be internally d-Calabi–Yau with respect to an idempotent.This definition abstracts properties of endomorphism algebras of $(d-1)$-cluster-tilting objects in certain stably $(d-1)$-Calabi–Yau Frobenius categories, as observed by Keller–Reiten.We show that an internally d-Calabi–Yau algebra … 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 ...

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 ... 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 …

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 ... 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 …

WebAllowing the Cluster. Users have to explicitly allow the cluster with this line in their Tiltfile: allow_k8s_contexts('my-cluster-name') If your cluster is a dev-only cluster that you …

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 … slang word for thiefWebIntroduction Tilting Cluster-tilting ˝-tiltingBibliography Setup isaﬁnite-dimensionalalgebraover k= . mod isthecategoryofﬁnitelygeneratedleft -modules. proj … slang word for underwearWebApr 8, 2016 · DOI: 10.2140/pjm.2024.289.449 Corpus ID: 119309242; Cluster tilting modules and noncommutative projective schemes @article{Ueyama2016ClusterTM, … slang word for whoreWebThus the existence of an n-cluster tilting module for selﬁnjective algebras gives global information on the whole module category. In [EH08, Section 5.5] the authors posed the … slang word for vagina beginning with gWebAn 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 ... slang word meaning trenchesWebMay 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 ... slang word for towel slang word normalization