Note on Categories of Indecomposable Modules
Manabu Harada (1972)
Publications du Département de mathématiques (Lyon)
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Manabu Harada (1972)
Publications du Département de mathématiques (Lyon)
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Pin Liu, Yunli Xie (2016)
Colloquium Mathematicae
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This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in and let Γ be the endomorphism algebra of R. Let F be the functor . We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in via F, and in turn, that projection from to mod Γ sends the maximal rigid objects which have no direct summands...
S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pish Hesari (2012)
Colloquium Mathematicae
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We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if , where R’ is a hereditary right R-module. Examples illustrating the results are presented.
Manabu Harada (1974)
Publications du Département de mathématiques (Lyon)
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Oleksandr Khomenko, Volodymyr Mazorchuk (2002)
Colloquium Mathematicae
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We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).
Xiaohui Zhang, Wei Wang, Juzhen Chen (2024)
Czechoslovak Mathematical Journal
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The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new -monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.
Roman Sikorski (1971)
Colloquium Mathematicae
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Aslak Bakke Buan (2001)
Colloquium Mathematicae
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We show that there is a one-to-one correspondence between basic cotilting complexes and certain contravariantly finite subcategories of the bounded derived category of an artin algebra. This is a triangulated version of a result by Auslander and Reiten. We use this to find an existence criterion for complements to exceptional complexes.
Daniel Simson
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CONTENTS1. Introduction.......................................................................................52. Traced rings and adjusted modules..................................................93. Moduled categories.........................................................................214. Triangular adjustments....................................................................325. Categories of matrices and -matrix modules...............436. Trace and cotrace reductions.........................................................477....
Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)
Colloquium Mathematicae
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Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).
Pasha Zusmanovich (2019)
Communications in Mathematics
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Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2016)
Colloquium Mathematicae
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We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.
Clezio A. Braga, Flávio U. Coelho (2009)
Colloquium Mathematicae
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We study the problem of when a direct limit of tilting modules is still a tilting module.
Alberto Facchini (1985)
Acta Universitatis Carolinae. Mathematica et Physica
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Mladen Bozicevic (1994)
Manuscripta mathematica
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Erik Backelin, Kobi Kremnitzer (2015)
Journal of the European Mathematical Society
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We prove a singular version of Beilinson–Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case settled by [BMR06]. We apply this theory to translation functors, singular blocks in the Bernstein–Gelfand–Gelfand category O and Whittaker modules.
Markus Schmidmeier (2002)
Czechoslovak Mathematical Journal
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We investigate the category of finite length modules over the ring , where is a V-ring, i.e. a ring for which every simple module is injective, a subfield of its centre and an elementary -algebra. Each simple module gives rise to a quasiprogenerator . By a result of K. Fuller, induces a category equivalence from which we deduce that . As a consequence we can (1) construct for each elementary -algebra over a finite field a nonartinian noetherian ring such that ,...