Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and their Completions
AbstractLet ℤ denote the integers and \(R = \coprod\nolimits_{i \in \mathbb{Z}} {{R_i}} \) a ℤ-graded commutative ring with R0 = k a field, Ri = (0) when i< 0, and where R is generated as a...
View ArticleCohen-Macaulay and Gorenstein Artin algebras
AbstractThe notions of Cohen-Macaulay and Gorenstein rings, as well as Cohen-Macaulay modules, are well established in commutative noetherian ring theory. In [6] we introduced similar notions for artin...
View ArticleQuasitilted Algebras
AbstractFor classes of algebras defined in nonhomological terms it is often of interest to look for a homological description. For example the Auslander algebras, that is the algebras which are...
View ArticleGrothendieck Groups and Tilting Objects
AbstractLet C be a connected Noetherian hereditary Abelian category with a Serre functor over an algebraically closed field k, with finite-dimensional homomorphism and extension spaces. Using the...
View ArticleHereditary noetherian categories of positive Euler characteristic
AbstractWe develop the fundamentals of hereditary noetherian categories with Serre duality over an arbitrary field k, where the category of coherent sheaves over a smooth projective curve over k serves...
View ArticleFrom m -clusters to m -noncrossing partitions via exceptional sequences
AbstractLet W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number...
View ArticleDynkin and Extended Dynkin Diagrams
AbstractIn this paper we give a survey of some of the occurrences of Dynkin and extended Dynkin diagrams in algebra. It is based on my lecture at the INdAM day in 2009, with some later developments...
View ArticleRigid and Schurian modules over cluster-tilted algebras of tame type
AbstractWe give an example of a cluster-tilted algebra \(\Lambda \) with quiver Q, such that the associated cluster algebra \(\mathcal {A}(Q)\) has a denominator vector which is not the dimension...
View ArticleDominant dimension and tilting modules
AbstractWe study which algebras have tilting modules that are both generated and cogenerated by projective–injective modules. Crawley–Boevey and Sauter have shown that Auslander algebras have such...
View Article
