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On the Almost Split Sequences for Relatively Projective Modules Over a Finite Group
| Content Provider | Scilit |
|---|---|
| Author | Kleiner, Mark |
| Copyright Year | 1992 |
| Description | Let $G$ be a finite group with a subgroup $H$. Given a field $k$ of characteristic $p$ dividing the order of $G$, denote by $\bmod kG$ the category of finite-dimensional over $k$ left $G$-modules, and let $\mathcal {C}$ be the full subcategory of $\bmod kG$ determined by the relatively projective modules. Let $0 \to L \to M \to N \to 0$ be an exact sequence in $\bmod kG$ with $L,M,N \in \mathcal {C}$. It is proved that the sequence is an almost split sequence in $\mathcal {C}$ if and only if it is an almost split sequence in $\bmod kG$. This implies, together with a recent result of Carlson and Happel, that $\mathcal {C}$ has almost split sequences if and only if it is closed under extensions, i.e., if and only if $p$ is coprime to either the order of $H$ or the index of $H$ in $G$. |
| Related Links | https://www.ams.org/proc/1992-116-04/S0002-9939-1992-1100656-X/S0002-9939-1992-1100656-X.pdf |
| Ending Page | 947 |
| Page Count | 5 |
| Starting Page | 943 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2159471 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 4 |
| Volume Number | 116 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1992-12-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Finite Group Split Sequence Projective Modules Recent Result Exact Sequence Finite Dimensional Full Subcategory Happel |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
