Über kohärente Ringe.
Direkte Produkte von freien Moduln.
Nilpotente Elemete in Ringen von endlicher globaler Dimension.
Halberbliche Endomorphismenringe.
Flache und halbinjektive Funktoren.
Additive functions for quivers with relations
Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when...
On selfinjective algebras of Euclidean type
Roots of Nakayama and Auslander-Reiten translations
We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.
Quasi-tilted algebras of canonical type
Selfinjective algebras of wild canonical type
We develop the representation theory of selfinjective algebras which admit Galois coverings by the repetitive algebras of algebras whose derived category of bounded complexes of finite-dimensional modules is equivalent to the derived category of coherent sheaves on a weighted projective line with virtual genus greater than one.
Homological Dimension and representation type of algebras under base field extension.
Extremal properties for concealed-canonical algebras
Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting bundles on...
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
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