Cup products on the complete relative cohomologies of finite groups and group algebras
type: Item
instance of: scholarly article
title: Cup products on the complete relative cohomologies of finite groups and group algebras
zbMATH Open document ID: 0943.20051
author: T. Nozawa
author: Katsunori Sanada
published in: Hokkaido Mathematical Journal
publication date: 2000-06-14T00:00:00Z
review text: A cup product on the complete relative cohomology \(H^*(\mathbb{Z} G,\mathbb{Z} K;A)\) of the group algebra \(\mathbb{Z} G\) of a finite group \(G\) has been defined by the first author [Tsukuba J. Math. 17, No. 1, 99-113 (1993; Zbl 0793.13005)]. The authors define a cup product on the complete relative cohomology \(H^*(G,K;M)\) of a finite group \(G\) and show an isomorphism between these cohomology groups preserving cup products. In particular, it follows that the ring \(H^*(G,K;\mathbb{Z})\) is a direct summand of the ring \(H^*(\mathbb{Z} G,\mathbb{Z} K;\mathbb{Z} G)\).
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18G25
zbMATH DE Number: 1396098
zbMATH Keywords: cup products
zbMATH Keywords: complete (co)homology
zbMATH Keywords: Tate cohomology
zbMATH Keywords: relative (co)homology
zbMATH Keywords: cohomology rings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001236
OpenAlex ID: W2044671071
DOI: 10.14492/HOKMJ/1351001236
Recommended article: Q4704855
Recommended article: Finite groups acting linearly: Hochschild cohomology and the cup product.
Recommended article: Cup product in bounded cohomology of the free group
Recommended article: Q4206843
Recommended article: Q6090859
Recommended article: Cup products, the Heisenberg group, and codimension two algebraic cycles
Recommended article: Cup-product in Hom-Leibniz cohomology and Hom-Zinbiel algebras
Recommended article: Q5483268
Recommended article: The cup product and coproduct for a combinatorially aspherical group
Recommended article: Cup coproducts in Hopf cyclic cohomology
description: scientific article; zbMATH DE number 1396098