-radicals and -radicals in the category of modules.
Tame algebras with strongly simply connected Galois coverings
Tensor products of higher almost split sequences in subcategories
We introduce the algebras satisfying the condition. If , are algebras satisfying the , condition, respectively, we give a construction of -almost split sequences in some subcategories of by tensor products and mapping cones. Moreover, we prove that the tensor product algebra satisfies the condition for some integers , ; this construction unifies and extends the work of A. Pasquali (2017), (2019).
The Auslander generators of the exterior algebra in two variables
We compute a complete set of nonisomorphic minimal Auslander generators for the exterior algebra in two variables.
The canonical algebras
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.
The Chu construction.
The construction of -solvable Abelian groups
The Hermitian Morita theorems.
The Kiew Algorithm for bocses applies directly to representation-finite algebras.
The Local Duality for Homomorphisms and an Application to Pure Semisimple PI-Rings
The pure-projective ideal of a module category
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The structure of Morita dual monoids.
The symplectic Gram-Schmidt theorem and fundamental geometries for -modules
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf is appropriately chosen) shows that symplectic -morphisms on free -modules of finite rank, defined on a topological space , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if is an -module (with respect to a -algebra sheaf without zero divisors) equipped with an orthosymmetric -morphism, we show, like in the classical...
The Ziegler spectrum of a tame hereditary algebra
Thick subcategories of the stable module category
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 Modules of Finite Projective Dimension.
Tilting sheaves in representation theory of algebras.