Gluing support tau-tilting object
WebAug 12, 2024 · On the other hand, for a basic support \(\tau \)-tilting pair (M, P), M is a \(\tau \)-tilting \(A/\langle e_P\rangle \)-module, where \(e_P\) is the idempotent of A associated to P. The support \(\tau \) -tilting A -modules have close relation with 2-term silting objects in the perfect derived category \({\textsf {per} }\,A\) of A . WebJul 3, 2024 · Abstract. An algebra is said to be $\tau$ -tilting finite provided it has only a finite number of $\tau$ -rigid objects up to isomorphism.To each such algebra, we associate a category whose objects are the wide subcategories of its category of finite dimensional modules, and whose morphisms are indexed by support $\tau$ -tilting pairs.
Gluing support tau-tilting object
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WebIntroduction Tilting Cluster-tilting ˝-tiltingBibliography Setup isafinite-dimensionalalgebraover k= . mod isthecategoryoffinitelygeneratedleft -modules. WebDefine gluing. gluing synonyms, gluing pronunciation, gluing translation, English dictionary definition of gluing. n. 1. a. A strong liquid adhesive obtained by boiling …
WebGlueing is a spelling variant of the same word, but it is an incorrect variant. Glueing is not the accepted spelling of this word in either American or British English. For reference, … WebAug 15, 2015 · τ. -tilting modules over endomorphism algebras of rigid objects. We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic ...
WebLet $(\mbox{mod} \Lambda',\mbox{mod} \Lambda,\mbox{mod} \Lambda")$ be a recollement of abelian categories for artin algebras $\Lambda'$, $\Lambda$ and $\Lambda"$. Under … WebWe succeed in generalizing this for any algebras, introducing wide $\tau$-tilting modules, a $\tau$-tilting object in some functorially finite wide subcategory. To achieve this, we study ICE-closed subcategories via the hearts of intervals in the lattice of torsion classes (we borrow the word heart from the Tattar’s paper, and is used in ...
WebFeb 15, 2024 · We introduce the higher version of Adachi-Iyama-Reiten's support τ-tilting pairs, which are regarded as a generalization of maximal τ n-rigid pairs in the sense of Jacobsen-Jørgensen.Assume that C is an (n + 2)-angulated category with an n-suspension functor Σ n and T is an Opperman-Thomas cluster tilting object. We prove that relative …
WebH. Enomoto, A. Sakai ICE-closed subcategories and wide $\tau$-tilting modules, ( arXiv:2010.05433) In the previous paper, I classified ICE-closed subcategories over hereditary algebras via partial tilting modules. We succeed in generalizing this for any algebras, introducing wide $\tau$-tilting modules, a $\tau$-tilting object in some ... ccrt teamWebThe notion "ghost tilting" is changed as "relative cluster tilting" due to the suggestion of the referee, thus the title has been changed in the present form. Final version to appear in Trans.AMS Subjects: ccrt therapy dialysisWebMay 20, 2024 · Gluing support. -tilting modules via symmetric ladders of height 2. Recent result by Adachi-Iyama-Reiten has shown a bijective correspondence between support … ccrt senior scholarshipWebFeb 11, 2024 · A Category of Wide Subcategories. An algebra is said to be $\tau$-tilting finite provided it has only a finite number of $\tau$-rigid objects up to isomorphism. To each such algebra, we associate a category whose objects are the wide subcategories of its category of finite dimensional modules, and whose morphisms are indexed by support … butch barry firedWebOct 12, 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. We show the same result if n is even and d ... ccrt treatmentWebAn 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 … butch barry wikipediaWebOct 3, 2012 · The aim of this paper is to introduce tau-tilting theory, which completes (classical) tilting theory from the viewpoint of mutation. It is well-known in tilting theory that an almost complete tilting module for any finite dimensional algebra over a field k is a direct summand of exactly 1 or 2 tilting modules. An important property in cluster tilting … ccrt therapy คือ