Algebras and Quaternion Defect Groups. II.
Algebras and Quaternion Defect Groups. I.
Tensor Products and Dimensions of simple Modules for Symmetric Groups.
Ext1 for Eyl modules of SL2 (K).
Projective Modules in Blocks with Elementary Abelian Defect Groups.
On a class of tame symmetric algebras having only periodic modules
On tubes for blocks of wild type
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.
The periodicity conjecture for blocks of group algebras
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.
Blocks with Dihedral Defect Groups in Solvable Groups.
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...
Relative Auslander-Reiten sequences for quasi-hereditary algebras
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).
Blocks for symmetric groups and their covering groups and quadratic forms.
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