Page 1 Next

Displaying 1 – 20 of 69

Showing per page

Tame tensor products of algebras

Zbigniew Leszczyński, Andrzej Skowroński (2003)

Colloquium Mathematicae

With the help of Galois coverings, we describe the tame tensor products A K B 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

Daniel Simson (1999)

Colloquium Mathematicae

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 Λ (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order Λ to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders Λ of non-polynomial growth are completely described in Theorem 6.2 and Corollary...

Tame triangular matrix algebras

Zbigniew Leszczyński, Andrzej Skowroński (2000)

Colloquium Mathematicae

We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra T 2 ( A ) of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which T 2 ( A ) 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

Stanisław Kasjan (2002)

Colloquium Mathematicae

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 Λ 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 q Λ associated with Λ in [26] is weakly non-negative. The result generalizes a criterion for tameness of such orders given by Simson [28] and gives an...

The combinatorics of quiver representations

Harm Derksen, Jerzy Weyman (2011)

Annales de l’institut Fourier

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 component quiver of a self-injective artin algebra

Alicja Jaworska, Andrzej Skowroński (2011)

Colloquium Mathematicae

We prove that the component quiver Σ A of a connected self-injective artin algebra A of infinite representation type is fully cyclic, that is, every finite set of components of the Auslander-Reiten quiver Γ A of A lies on a common oriented cycle in Σ A .

Currently displaying 1 – 20 of 69

Page 1 Next