Coxeter transformation and inverses of Cartan matrices for coalgebras
| dc.creator | Chin, William | |
| dc.creator | Simson, Daniel | |
| dc.date | 2009-04-10 | |
| dc.date.accessioned | 2026-07-07T13:03:15Z | |
| dc.date.available | 2026-07-07T13:03:15Z | |
| dc.description | Let C be a coalgebra and consider the Grothendieck groups of the categories of the socle-finite injective right and left C-comodules. One of the main aims of the paper is to study Coxeter transformation, and its dual, of a pointed sharp Euler coalgebra C, and to relate the action of these transformations on a class of indecomposable finitely cogenerated C-comodules N with almost split sequences starting or ending with N. We also show that if C is a pointed K-coalgebra such that the every vertex of the left Gabriel quiver of C has only finitely many neighbours, then for any indecomposable non-projective left C-comodule N of finite K-dimension, there exists a unique almost split sequence of finitely cogenerated left C-comodules ending at N. We show that the dimension vector of the Auslander-Reiten translate given by the Coxeter transformation, if C is hereditary, or more generally, if inj.dim DN=1 and Hom(C,DN)=0. | |
| dc.identifier | https://arxiv.org/abs/0904.1765 | |
| dc.identifier | http://arxiv.org/abs/0904.1765 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226734 | |
| dc.subject | Representation Theory | |
| dc.subject | K-Theory and Homology | |
| dc.title | Coxeter transformation and inverses of Cartan matrices for coalgebras | |
| dc.type | text |