Euclidean components for a class of self-injective algebras

• Autorzy: Sarah Scherotzke
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16E20: Grothendieck groups, K -theory, etc.
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
• 16S40: Smash products of general Hopf actions
• 16G10: Representations of Artinian rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 115
• Numer: 2
• Strony: 219-245

Daty

wydano

2009

Twórcy

autor

Sarah Scherotzke

• Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom

Identyfikatory

DOI

10.4064/cm115-2-7