Generalized tilting theory
WebSep 6, 2024 · Tilting Theory: A Gift of Representation Theory to Mathematics Gabriella D’Este The Mathematical Intelligencer 39 , 77–86 ( 2024) Cite this article 1589 Accesses … WebarXiv:1208.2803v3 [math.RT] 25 Feb 2013 GENERALIZED TILTING THEORY PEDRO NICOLAS AND MANUEL SAOR´ ´IN Dedicated to the memory of Michael Butler and …
Generalized tilting theory
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WebFeb 1, 2007 · Math. 470 (1996) 51–85] is generalized to the tilting module case by giving an isomorphism between two Ringel–Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113–146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. WebTilting theory enters the picture as a rich source of derived equivalences. Indeed, according to a theorem by D. Happel, if B is an algebra and T a tilting module for B with …
Webfrom the theory of triangulated categories. In Section 2 we introduce the notion of a generalized tilting module for rings and show how it gives rise to equivalences of certain derived categories. The main theorem of this sec- tion, Theorem 2.1, represents an extension and generalization of a result a WebJun 7, 2010 · In representation theory of algebras and groups, finitely generated tilting modules have successfully been applied to understanding different aspects of algebraic and homological structure and...
WebOct 10, 2024 · As to the general tilting modules of finite projective dimension, it was often asked whether the. ... We extend interesting results in the tilting theory to semi-tilting complexes. As corollaries ... WebUsing the same methods, Keller [36] generalized tilting theory to di erential-graded (dg) algebras and gave a very simple criterion for an object T in a triangu-lated category Dto give an equivalence with the derived category of the dg algebra ... this thesis, such as tilting theory, Koszul duality, compact objects, and braid group actions. For ...
WebJul 1, 2024 · Tilting theory goes back to the work of I.N. Bernshtein, I.M. Gel'fand and V.A. Ponomarev on the characterization of representation-finite hereditary algebras through their ordinary quivers (cf. also Quiver ). Their reflection functors on quivers has led to a module-theoretical interpretation by M. Auslander, M.I. Platzeck and I. Reiten.
WebJul 7, 2013 · Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. oncallsetupWebJul 1, 2024 · The success of this strategy to study a bigger class of algebras through tilting theory has led to several generalizations. On one hand, one can relax the condition on … oncall services incWebDec 1, 1986 · In Section 1 we briefly recall some standard notation and constructions from the theory of triangulated categories. In Section 2 we introduce the notion of a … on call screen connectWebIn terms of representation theory, τ-tilting theory has given new ways of describing the module category of a finite dimensional algebra by establishing bijections between τ-tilting pairs, functorially finite torsion classes and 2-term silting complexes. on-call servicenowWebAug 1, 2013 · We deal with the notion of a generalized tilting subcategory T of the category Mod ( C ) of contravariant functors from a skeletally small preadditive category C , to the category of abelian groups. on call service center clearwaterWebMay 15, 2024 · Geigle, W., Lenzing, H.: A class of weighted projective lines arising in the representation theory of finite dimensional algebras. Springer Lecture Notes in Mathematics 1273, 265–297 (1987) Geigle, W., Lenzing, H.: Perpendicular categories … is athlete\u0027s foot is a communicable diseaseWebMay 1, 2004 · We show the left Γ-module U = Γ Ⓧr C with the endmorphism ring EndΓU = Δ is a generalized tilting module when RC is a generalized tilting module under some conditions. PDF. Save. Alert. ω-Gorenstein injective modules and dimensions. ... Tilting theory is known as a powerful tool for studying representation theory of artin algebras. oncall shevingron