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Subcategories of the derived category and cotilting complexes

Aslak Bakke Buan (2001)

Colloquium Mathematicae

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.

Subproducts defined by means of subdirect products

Frans Loonstra (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si supponga che l'anello 𝐑 ammetta una decomposizione come prodotto subdiretto 𝐑 = × α 𝚲 ~ 𝐑 α di anelli 𝐑 α 𝟎 , tali che per 𝐒 α = 𝐑 𝐑 α si abbia Ann 𝐑 α 𝐒 α = 𝟎 ( α A ), e sia 𝐒 = α 𝐀 𝐒 α . Si scelga un 𝐑 -modulo (destro) 𝐌 che sia libero da torsione rispetto ad 𝐒 , cioè Ann 𝐌 𝐒 = 𝟎 ; allora 𝐌 può essere rappresentato come prodotto subdiretto irridondante 𝐌 × α 𝚲 ~ 𝐌 α degli 𝐑 α -moduli 𝐌 α liberi da torsione rispetto ad 𝐒 α . Si fa uno studio di un subprodotto generale di una classe 𝐂 di 𝐑 -moduli 𝐌 ( 𝐢 ) ...

Substructures of algebras with weakly non-negative Tits form.

José Antonio de la Peña, Andrzej Skowronski (2007)

Extracta Mathematicae

Let A = kQ/I be a finite dimensional basic algebra over an algebraically closed field k presented by its quiver Q with relations I. A fundamental problem in the representation theory of algebras is to decide whether or not A is of tame or wild type. In this paper we consider triangular algebras A whose quiver Q has no oriented paths. We say that A is essentially sincere if there is an indecomposable (finite dimensional) A-module whose support contains all extreme vertices of Q. We prove that if...

Sur certaines algèbres de Lie de dérivations

Yves Félix, Stephen Halperin, Jean-Claude Thomas (1982)

Annales de l'institut Fourier

Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.

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