Dual Gabriel Theorem with applications
| dc.creator | Chen, Xiao-Wu | |
| dc.creator | Huang, Hua-Lin | |
| dc.creator | Zhang, Pu | |
| dc.date | 2004-01-17 | |
| dc.date | 2004-12-28 | |
| dc.date.accessioned | 2026-07-07T06:34:15Z | |
| dc.date.available | 2026-07-07T06:34:15Z | |
| dc.description | We introduce the quiver of a bicomodule over a cosemisimple coalgebra. Applying this to the coradical $C_0$ of an arbitrary coalgebra $C$, we give an alternative definition of the Gabriel quiver of $C$, and then show that it coincides with the known $\operatorname {Ext}$ quiver of $C$ and the link quiver of $C$. The dual Gabriel theorem for a coalgebra with separable coradical is obtained, which generalizes the corresponding result for a pointed coalgebra. We also give a new description of $C_1$ of any coalgebra $C$, which can be regarded as a generalization of the first part of the well-known Taft-Wilson Theorem for pointed coalgebras. As applications, we give a characterization of locally finite coalgebras via their Gabriel quivers, and a property of the Gabriel quiver of a quasi-coFrobenius coalgebra. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0401214 | |
| dc.identifier | http://arxiv.org/abs/math/0401214 | |
| dc.identifier | Science in China, Series A Mathematics, (2006) Vol. 49 (1), 9-26. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99465 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | Dual Gabriel Theorem with applications | |
| dc.type | text |