Algebras whose Euler form is non-negative
Almost split sequences and module categories: A complementary view to Auslander-Reiten Theory
We take a complementary view to the Auslander-Reiten trend of thought: Instead of specializing a module category to the level where the existence of an almost split sequence is inferred, we explore the structural consequences that result if we assume the existence of a single almost split sequence under the most general conditions. We characterize the structure of the bimodule with an underlying ring solely assuming that there exists an almost split sequence of left -modules . and are...
An alternate criterion of colocalized-localized modules.
The aim of this note is to express a module which is localized as well as colocalized in terms of an object of an intersecting subcategory related to static modules.
An example of two von Neumann regular rings with nonisomorphic Monta equivalent multiplicative semigroups.
An explicit construction for the Happel functor
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.
Auslander-Reiten components for concealed-canonical algebras
Auslander-Reiten triangles in derived categories.
Bicovariant differential calculi and cross products on braided Hopf algebras
In a braided monoidal category C we consider Hopf bimodules and crossed modules over a braided Hopf algebra H. We show that both categories are equivalent. It is discussed that the category of Hopf bimodule bialgebras coincides up to isomorphism with the category of bialgebra projections over H. Using these results we generalize the Radford-Majid criterion and show that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. In specific braided monoidal...
Bipartite coalgebras and a reduction functor for coradical square complete coalgebras
Let C be a coalgebra over an arbitrary field K. We show that the study of the category C-Comod of left C-comodules reduces to the study of the category of (co)representations of a certain bicomodule, in case C is a bipartite coalgebra or a coradical square complete coalgebra, that is, C = C₁, the second term of the coradical filtration of C. If C = C₁, we associate with C a K-linear functor that restricts to a representation equivalence , where is a coradical square complete hereditary bipartite...
Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations
A class of stratified posets is investigated and their incidence algebras are studied in connection with a class of non-shurian vector space categories. Under some assumptions on we associate with a bound quiver (Q, Ω) in such a way that . We show that the fundamental group of (Q, Ω) is the free group with two free generators if is rib-convex. In this case the universal Galois covering of (Q, Ω) is described. If in addition is three-partite a fundamental domain of this covering is...
Bounded Picard groups
Calabi-Yau stable module categories of finite type
We describe the stable module categories of the self-injective finite-dimensional algebras of finite representation type over an algebraically closed field which are Calabi-Yau (in the sense of Kontsevich).
Categorical methods in graded ring theory.
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.
Character modules, submodules of a free module, and quasi-Frobenius rings.
Classes of Modules.
Classes of modules related to Serre subcategories.
Coalgebras, braidings, and distributive laws.
Coherent Rings and Homologically Finite Subcategories.
Colimits of representable algebra-valued functors.
Comparison of abelian categories recollements.