Chen, Bo (2011). The number of the Gabriel-Roiter measures admitting no direct predecessors over a wild quiver. J. Pure Appl. Algebr., 215 (10). S. 2341 - 2352. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 0022-4049
Full text not available from this repository.Abstract
A famous result by Drozd says that a finite-dimensional representation-infinite algebra is of either tame or wild representation type. But one has to make assumption on the ground field. The Gabriel-Roiter measure might be an alternative approach to extend these concepts of tame and wild to arbitrary Artin algebras. In particular, the infiniteness of the number of GR segments, i.e. sequences of Gabriel-Roiter measures which are closed under direct predecessors and successors, might relate to the wildness of Artin algebras. As the first step, we are going to study the wild quiver with three vertices, labeled by 1, 2 and 3, and one arrow from 1 to 2 and two arrows from 2 to 3. The Gabriel-Roiter submodules of the indecomposable preprojective modules and quasi-simple modules tau(-iM), i >= 0 are described, where M is a Kronecker module and tau = DTr is the Auslander-Reiten translation. Based on these calculations, the existence of infinitely many GR segments will be shown. Moreover, it will be proved that there are infinitely many Gabriel-Roiter measures admitting no direct predecessors. (C) 2010 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-488765 | ||||||||
| DOI: | 10.1016/j.jpaa.2010.12.014 | ||||||||
| Journal or Publication Title: | J. Pure Appl. Algebr. | ||||||||
| Volume: | 215 | ||||||||
| Number: | 10 | ||||||||
| Page Range: | S. 2341 - 2352 | ||||||||
| Date: | 2011 | ||||||||
| Publisher: | ELSEVIER SCIENCE BV | ||||||||
| Place of Publication: | AMSTERDAM | ||||||||
| ISSN: | 0022-4049 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/48876 |
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