Tate Cohomology Group
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High Quality Content by WIKIPEDIA articles! In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. The study of fixed points of groups acting on modules and quotient modules is a motivation, but the cohomology can be defined using various constructions. There is a dual theory, group homology, and a generalization to non-abelian coefficients. These algebraic ideas are closely related to topological ideas. A great deal is known about…mehr

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High Quality Content by WIKIPEDIA articles! In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. The study of fixed points of groups acting on modules and quotient modules is a motivation, but the cohomology can be defined using various constructions. There is a dual theory, group homology, and a generalization to non-abelian coefficients. These algebraic ideas are closely related to topological ideas. A great deal is known about the cohomology of groups, including interpretations of low dimensional cohomology, functorality, and how to change groups. The history of group cohomology began in the 1920s, matured in the late 1940s, and continues as an area of active research today.