Euclidean components for a class of self-injective algebras
| dc.creator | Scherotzke, Sarah | |
| dc.date | 2008-09-08 | |
| dc.date | 2008-11-07 | |
| dc.date.accessioned | 2026-07-07T10:16:17Z | |
| dc.date.available | 2026-07-07T10:16:17Z | |
| dc.description | We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. 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 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 with a commutative semi-simple group algebra to have components with Euclidean tree class, depending on the components of the Auslander-Reiten quiver of the basic algebra. We also develop some properties of the bilinear form dim Hom_A(-,-) for the representation ring G(A) of any finite-dimensional algebra A. | |
| dc.description | 26 pages, to appear in Colloquium Mathematicum, some typos corrected | |
| dc.identifier | https://arxiv.org/abs/0809.1376 | |
| dc.identifier | http://arxiv.org/abs/0809.1376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173454 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | Euclidean components for a class of self-injective algebras | |
| dc.type | text |