Results 81 to 90 of about 2,140 (101)

Representation-Finite Algebras whose Auslander-Reiten Quiver is Planar

Journal of the London Mathematical Society, 1985
For a finite representation type algebra A we study conditions on the Gabriel quiver with relations of A, which allow to decide if the Auslander-Reiten quiver of A has oriented cycles or not. Our conditions give a constructive characterization of the representation-finite algebras whose Auslander-Reiten quiver have no oriented cycle and which have at ...
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Stratification of Finite Auslander-Reiten Quivers Without Oriented Cycles

Journal of the London Mathematical Society, 1985
Let \(R\) be a representation-finite finite-dimensional algebra over an algebraically closed field \(K\) whose Auslander-Reiten translation quiver \((\Gamma,\tau)\) has no oriented cycles. It is shown that \(\Gamma\) admits a stratification, that is, a map \(h\) from the set \(\Gamma_ 0\) of vertices of \(\Gamma\) to \(N\) satisfying the following ...
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The Auslander-Reiten quiver of a finite group

Archiv der Mathematik, 1985
Let G be a finite group, p a prime and k a field of characteristic p. The Auslander-Reiten quiver of the group ring kG, denoted A(kG), is the directed graph whose vertices are the isomorphism classes of indecomposable kG-modules, and if M and N are indecomposable kG-modules, then there is an edge \(M\to N\) if and only if there is an irreducible map ...
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Auslander-Reiten Quivers of Algebras whose Indecomposable Modules are Bricks

Bulletin of the London Mathematical Society, 1991
Let \(A\) be a finite dimensional basic algebra over an algebraically closed field \(k\) and let \(1=\sum^ r_{i=1}e_ i\) be a decomposition of the unit element of \(A\) into primitive orthogonal idempotents. For given \(e_ i\) let \(\Gamma_ i\) be the full translation subquiver of the Auslander-Reiten quiver of \(A\) supported by all indecomposable \(A\
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Endotrivial modules and the Auslander-Reiten quiver

1991
As Dade stated it in [8]: “There are just too many modules over p-groups!” More precisely, if P is a p-group and R a suitable commutative valuation ring, then almost always the group algebra RP is of wild representation type and there is no classification of all its indecomposable modules.
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The Auslander–Reiten-quiver

1995
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Many Algebras with the same Auslander-Reiten Quiver

Bulletin of the London Mathematical Society, 1983
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Auslander–Reiten Components with Sectional Bypasses

Communications in Algebra, 2009
Sonia Trepode
exaly  

On relative projectivity of lattices in Auslander-Reiten components for group rings

Communications in Algebra, 2020
Shigeto Kawata
exaly  

Auslander-Reiten Quivers for Certain Algebras of Finite Representation Type

Journal of the London Mathematical Society, 1982
Bautista, R., Larrion, F.
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