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Displaying 21 – 37 of 37

The representation dimension of domestic weakly symmetric algebras

Rafał Bocian, Thorsten Holm, Andrzej Skowroński (2004)

Open Mathematics

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras...

The shift functor and the comprehensive factorization for internal groupoids

Dominique Bourn (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The six operations for sheaves on Artin stacks II: Adic coefficients

Yves Laszlo, Martin Olsson (2008)

Publications Mathématiques de l'IHÉS

The structure of the tensor product of $𝔽_{2} [-]$ with a finite functor between $𝔽_{2}$ -vector spaces

Geoffrey M. L. Powell (2000)

Annales de l'institut Fourier

The paper studies the structure of functors $I \otimes F$ in the category of functors from finite dimensional $𝔽_{2}$ -vector spaces to $𝔽_{2}$ -vector spaces, where $F$ is a finite functor and $I$ is the injective functor $V \mapsto 𝔽_{2}^{V^{*}}$ . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors $I \otimes F$ are artinian of type one.

The Taylor spectrum and quotient Banach spaces

L. Waelbroeck (1982)

Banach Center Publications

Théorie des catégories semi-abéliennes

Jacques Riguet (1968/1969)

Séminaire Dubreil. Algèbre et théorie des nombres

Thick subcategories of the stable module category

D. Benson, Jon Carlson, Jeremy Rickard (1997)

Fundamenta Mathematicae

We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...

Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras

Lutz Hille, Markus Perling (2014)

Annales de l’institut Fourier

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$ . Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is equivalent to the bounded derived category of finitely generated modules over a finite dimensional quasi-hereditary algebra $A$ . The construction starts with a full exceptional sequence of line bundles on $X$ and uses universal extensions. If $X$ is any smooth projective variety...

Topological categories containing any category of algebras

Jan Reiterman, Věra Trnková (1977)

Czechoslovak Mathematical Journal

Topological linear compactness for Grothendieck categories. Theorem of Tychonoff. Applications to coalgebras.

P. Enache, C. Nastasescu, B. Torrecillas (2006)

Publicacions Matemàtiques

We show the Tychonoff's theorem for a Grothendieck category with a set of small projective generators. Strictly quasi-finite objects for semiartinian Grothendieck categories are characterized. We apply these results to the study of the Morita duality of dual algebra of a coalgebra.

Torsion Theories in Non-Additive Categories.

Basil A. Rattray (1974)

Manuscripta mathematica

Triangulated categories of periodic complexes and orbit categories

Jian Liu (2023)

Czechoslovak Mathematical Journal

We investigate the triangulated hull of orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull corresponds to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This specializes to Stai and Zhao’s result on the finite dimensional algebra of finite global dimension. As the first application, if $A$ , $B$ are flat algebras over a commutative...

Triples et exactitudes

Michel Hacque (1974)

Publications du Département de mathématiques (Lyon)

Truncated microsupport and holomorphic solutions of D-modules

Masaki Kashiwara, Teresa Monteiro Fernandes, Pierre Schapira (2003)

Annales scientifiques de l'École Normale Supérieure

Tubular mutations

Hagen Meltzer (1998)

Colloquium Mathematicae

Two notes on radicals of Abelian groups

Barry J. Gardner (1972)

Commentationes Mathematicae Universitatis Carolinae

Two results of $n$ -exangulated categories

Jian He, Jing He, Panyue Zhou (2024)

Czechoslovak Mathematical Journal

M. Herschend, Y. Liu, H. Nakaoka introduced $n$ -exangulated categories, which are a simultaneous generalization of $n$ -exact categories and $(n + 2)$ -angulated categories. This paper consists of two results on $n$ -exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an $n$ -exangulated category.

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