Higher Extension Modules and the Yoneda Product
| dc.creator | Barakat, Mohamed | |
| dc.creator | Bremer, Barbara | |
| dc.date | 2008-02-21 | |
| dc.date.accessioned | 2026-07-07T09:22:33Z | |
| dc.date.available | 2026-07-07T09:22:33Z | |
| dc.description | A chain of c submodules E =: E_0 >= E_1 >= ... >= E_c >= E_{c+1} := 0 gives rise to c composable 1-cocycles in Ext^1(E_{i-1}/E_i,E_i/E_{i+1}), i=1,...,c. In this paper we follow the converse question: When are c composable 1-cocycles induced by a module E together with a chain of submodules as above? We call such modules c-extension modules. The case c=1 is the classical correspondence between 1-extensions and 1-cocycles. For c=2 we prove an existence theorem stating that a 2-extension module exists for two composable 1-cocycles eta^M_L in Ext^1(M,L) and eta^L_N in Ext^1(L,N), if and only if their Yoneda product eta^M_L o eta^L_N in Ext^2(M,N) vanishes. We further prove a modelling theorem for c=2: In case the set of all such 2-extension modules is non-empty it is an affine space modelled over the abelian group that we call the first extension group of 1-cocycles, Ext^1(eta^M_L,eta^L_N) := Ext^1(M,N)/(Hom(M,L) o eta^L_N + eta^M_L o Hom(L,N)). | |
| dc.description | 23 pages including 5 small appendices on 4 pages | |
| dc.identifier | https://arxiv.org/abs/0802.3179 | |
| dc.identifier | http://arxiv.org/abs/0802.3179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155414 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 13D02; 13D05; 13D07; 16E05; 16E10; 16E30 | |
| dc.title | Higher Extension Modules and the Yoneda Product | |
| dc.type | text |