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Euclidean components for a class of self-injective algebras

100%

Scherotzke S.

Colloquium Mathematicum

2009

tom 115

nr 2

219-245

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 with Euclidean tree class if p = 2. Finally, we deduce conditions for a smash product of a local basic algebra Γ with a commutative semisimple group algebra to have components with Euclidean tree class, depending on the components of the Auslander-Reiten quiver of Γ.

Component clusters for acyclic quivers

100%

Scherotzke S.

Colloquium Mathematicum

2016

tom 144

nr 2

245-264

The theory of Caldero-Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schröer (2015) leads to a refinement of the notions of cluster variables and clusters, via so-called component clusters. We compare component clusters to classical clusters for the cluster algebra of an acyclic quiver. We propose a definition of mutation between component clusters and determine the mutation relations of component clusters for affine quivers. In the case of a wild quiver, we provide bounds for the size of component clusters.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Scherotzke S.

1 2016

1 2009

Wyniki wyszukiwania

Euclidean components for a class of self-injective algebras

Component clusters for acyclic quivers