Euclidean components for a class of self-injective algebras

Sarah Scherotzke. "Euclidean components for a class of self-injective algebras." Colloquium Mathematicae 115.2 (2009): 219-245. <http://eudml.org/doc/284288>.

@article{SarahScherotzke2009,
abstract = {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.},
author = {Sarah Scherotzke},
journal = {Colloquium Mathematicae},
keywords = {Auslander-Reiten theory; transitive algebras; Euclidean components; self-injective algebras; composition series of projective modules; Auslander-Reiten components; lengths of composition series; universal enveloping algebras},
language = {eng},
number = {2},
pages = {219-245},
title = {Euclidean components for a class of self-injective algebras},
url = {http://eudml.org/doc/284288},
volume = {115},
year = {2009},
}

TY - JOUR
AU - Sarah Scherotzke
TI - Euclidean components for a class of self-injective algebras
JO - Colloquium Mathematicae
PY - 2009
VL - 115
IS - 2
SP - 219
EP - 245
AB - 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.
LA - eng
KW - Auslander-Reiten theory; transitive algebras; Euclidean components; self-injective algebras; composition series of projective modules; Auslander-Reiten components; lengths of composition series; universal enveloping algebras
UR - http://eudml.org/doc/284288
ER -