Cohomologies of finite abelian groups

• Date: 2017
• Main Authors: Drozd, Yuriy A., Plakosh, Andriana I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: cohomologies; finite abelian groups; resolution; \(G\)-lattice; 20J06; 18G10; 20K01
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/530
• Journal Title: Algebra and Discrete Mathematics

We construct a simplified resolution for the trivial \(G\)-module \(\mathbb{Z}\), where \(G\) is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible \(G\)-lattices and their duals.