Representation and cohomologies of groups and semigroups

• Date: 2025
• Author Affiliations: Андріяна Плакош — Інститут математики НАН України
• Keywords: keywords
• Main Authors: Plakosh, Andriiana, Плакош, Андріяна
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2025
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/544
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

This article surveys results related to the cohomology of lattices over group rings, particularly over the group ring of the Klein four--group. It is shown that in this setting, syzygies coincide with the Auslander-Reiten translation, enabling the full computation of Tate cohomology for all lattices...