Tame algebras with strongly simply connected Galois coverings
Tame minimal non-polynomial growth simply connected algebras
Tame orders
Tame tensor products of algebras
With the help of Galois coverings, we describe the tame tensor products of basic, connected, nonsimple, finite-dimensional algebras A and B over an algebraically closed field K. In particular, the description of all tame group algebras AG of finite groups G over finite-dimensional algebras A is completed.
Tame three-partite subamalgams of tiled orders of polynomial growth
Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders of non-polynomial growth are completely described in Theorem 6.2 and Corollary...
Tame triangular matrix algebras
We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders
A criterion for tame prinjective type for a class of posets with zero-relations is given in terms of the associated prinjective Tits quadratic form and a list of hypercritical posets. A consequence of this result is that if is a three-partite subamalgam of a tiled order then it is of tame lattice type if and only if the reduced Tits quadratic form associated with in [26] is weakly non-negative. The result generalizes a criterion for tameness of such orders given by Simson [28] and gives an...
Tame-wild dichotomy for Cohen-Macaulay modules.
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).
Th normal decomposition of lattices and the Krull-Schmidt theorem.
The Algebraic and Geometric Classification of Associative Algebras of Dimension Five.
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 Auslander translate of a short exact sequence
The Auslander-Reiten quiver for posets of finite growth
The Auslander-Reiten quiver of a modular group algebra revisited.
The canonical algebras
The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.
The Cohomology Ring of a Monomial Algebra.
The combinatorics of quiver representations
We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically...
The completely separating incidence algebras of tame representation type
We prove that a completely separating incidence algebra of a partially ordered set is of tame representation type if and only if the associated Tits integral quadratic form is weakly non-negative.