Subcategories of the derived category and cotilting complexes

Aslak Bakke Buan

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Displaying similar documents to “Subcategories of the derived category and cotilting complexes”

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Relative theory in subcategories

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We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].

Algebraically compact modules

Alberto Facchini (1985)

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K. Erdmann, D. Madsen, V. Miemietz (2010)

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We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...

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The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple. ...

An explicit construction for the Happel functor

M. Barot, O. Mendoza (2006)

Colloquium Mathematicae

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An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.

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Manabu Harada (1974)

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Relative Auslander-Reiten sequences for quasi-hereditary algebras

Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)

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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).

On the structure of locally finite pure semisimple Grothendieck categories

Daniel Simson (1982)

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Krull-Gabriel dimension and Cantor-Bendixson rank of 1-domestic string algebras

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We prove that the Krull-Gabriel dimension of the category of modules over any 1-domestic non-degenerate string algebra is 3.

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Timothy Porter (1985)

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Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras

Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang (2016)

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We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of...

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Schwede, Stefan, Shipley, Brooke (2003)

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