Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the almost split sequences for relatively projective modules over a finite group


Author: Mark Kleiner
Journal: Proc. Amer. Math. Soc. 116 (1992), 943-947
MSC: Primary 16G70
DOI: https://doi.org/10.1090/S0002-9939-1992-1100656-X
MathSciNet review: 1100656
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16G70

Retrieve articles in all journals with MSC: 16G70


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1100656-X
Keywords: Almost split sequence, relatively projective module, finite group
Article copyright: © Copyright 1992 American Mathematical Society