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On tubes for blocks of wild type

100%
Erdmann K.
Colloquium Mathematicum
|
1999
|
tom 82
|
nr 2
261-270
EN
We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.
2
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On a class of tame symmetric algebras having only periodic modules

75%
Erdmann K.
Banach Center Publications
|
1990
|
tom 26
|
nr 1
287-302
3
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The periodicity conjecture for blocks of group algebras

64%
Erdmann K., Skowroński A.
Colloquium Mathematicum
|
2015
|
tom 138
|
nr 2
283-294
EN
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
4
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Relative Auslander-Reiten sequences for quasi-hereditary algebras

51%
Erdmann K., de la Peña J., Sáenz C.
Colloquium Mathematicum
|
2002
|
tom 91
|
nr 1
123-142
EN
Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).
5
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Deformed mesh algebras of Dynkin type ℂₙ

51%
Białkowski J., Erdmann K., Skowroński A.
Colloquium Mathematicum
|
2012
|
tom 126
|
nr 2
217-230
EN
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type 𝕃ₙ (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 $𝔸_{2n}$. 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 of simple plane curve singularities of type $𝔸_{2n-1}$. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂₙ.
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