Definition
If G is a finite group and A a G-module, then there is a natural map N from H0(G,A) to H0(G,A) taking a representative a to Σ g(a) (the sum over all G-conjugates of a). The Tate cohomology groups are defined by
- for n≥ 1.
- quotient of H0(G,A) by norms
- quotient of norm 0 elements of H0(G,A) by principal norm 0 elements
- for n≤ −2.
Read more about this topic: Tate Cohomology Group
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)