Covering Spaces in Representation-Theory.
Cycle-finite algebras of semiregular type
We describe the structure of artin algebras for which all cycles of indecomposable finitely generated modules are finite and all Auslander-Reiten components are semiregular.
Deformed mesh algebras of Dynkin type ℂₙ
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable Auslander algebras...
Degenerations for indecomposable modules and tame algebras
Degenerations for modules over representation-finite selfinjective algebras
Degenerations in the module varieties of almost cyclic coherent Auslander-Reiten components
We establish when the partial orders and coincide for all modules of the same dimension from the additive category of a generalized standard almost cyclic coherent component of the Auslander-Reiten quiver of a finite-dimensional algebra.
Degenerations in the Module Varieties of Generalized Standard Auslander-Reiten Components
Derived tubular algebras and APR-tilts
Die Vektorraumkategorie zu einem unzerlegbaren projektiven Modul einer tubularen Algebra.
Directing components for quasitilted algebras
We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
Domestic iterated one-point extensions of algebras by two-ray modules
In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of...
Elementary modules.
Endomorphism algebras of exceptional sequences over path algebras of type
Endomorphism rings of regular modules over wild hereditary algebras
Let H be a connected wild hereditary path algebra. We prove that if Z is a quasi-simple regular brick, and [r]Z indecomposable regular of quasi-length r and with quasi-top Z, then .
Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup
Let be a finite group with a Sylow 2-subgroup which is either quaternion or semi-dihedral. Let be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial -modules, whose restrictions to are isomorphic to the direct sum of the known exotic endotrivial -modules and some projective modules. This provides a description of the group of endotrivial -modules.
Euclidean components for a class of self-injective algebras
We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only allow components...
Finding a cluster-tilting object for a representation finite cluster-tilted algebra
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
Full embeddings of almost split sequences over split-by-nilpotent extensions
Let R be a split extension of an artin algebra A by a nilpotent bimodule , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if = 0 and .
Generalized canonical algebras and standard stable tubes
We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.
Generalized coil enlargements of algebras