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- Inflation-restriction_exact_sequence abstract "In mathematics, the inflation-restriction exact sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the study of spectral sequences.Specifically, let G be a group, N a normal subgroup, and A an abelian group which is equipped with an action of G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G/N acts on AN = { a ∈ A : na = a for all n ∈ N}. Then the inflation-restriction exact sequence is:0 → H 1(G/N, AN) → H 1(G, A) → H 1(N, A)G/N → H 2(G/N, AN) →H 2(G, A)In this sequence, there are maps inflation H 1(G/N, AN) → H 1(G, A) restriction H 1(G, A) → H 1(N, A)G/N transgression H 1(N, A)G/N → H 2(G/N, AN) inflation H 2(G/N, AN) →H 2(G, A)The inflation and restriction are defined for general n: inflation Hn(G/N, AN) → Hn(G, A) restriction Hn(G, A) → Hn(N, A)G/NThe transgression is defined for general n transgression Hn(N, A)G/N → Hn+1(G/N, AN)only if Hi(N, A)G/N = 0 for i ≤ n − 1.The sequence for general n may be deduced from the case n = 1 by dimension-shifting or from the Lyndon–Hochschild–Serre spectral sequence.".
- Inflation-restriction_exact_sequence wikiPageID "31364787".
- Inflation-restriction_exact_sequence wikiPageLength "4033".
- Inflation-restriction_exact_sequence wikiPageOutDegree "16".
- Inflation-restriction_exact_sequence wikiPageRevisionID "705929301".
- Inflation-restriction_exact_sequence wikiPageWikiLink Abelian_group.
- Inflation-restriction_exact_sequence wikiPageWikiLink Automorphism.
- Inflation-restriction_exact_sequence wikiPageWikiLink Cambridge_University_Press.
- Inflation-restriction_exact_sequence wikiPageWikiLink Category:Homological_algebra.
- Inflation-restriction_exact_sequence wikiPageWikiLink Exact_sequence.
- Inflation-restriction_exact_sequence wikiPageWikiLink Five-term_exact_sequence.
- Inflation-restriction_exact_sequence wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Inflation-restriction_exact_sequence wikiPageWikiLink Group_(mathematics).
- Inflation-restriction_exact_sequence wikiPageWikiLink Group_cohomology.
- Inflation-restriction_exact_sequence wikiPageWikiLink Homomorphism.
- Inflation-restriction_exact_sequence wikiPageWikiLink Lyndon–Hochschild–Serre_spectral_sequence.
- Inflation-restriction_exact_sequence wikiPageWikiLink Normal_subgroup.
- Inflation-restriction_exact_sequence wikiPageWikiLink Spectral_sequence.
- Inflation-restriction_exact_sequence wikiPageWikiLink Springer_Science+Business_Media.
- Inflation-restriction_exact_sequence wikiPageWikiLinkText "Inflation-restriction exact sequence".
- Inflation-restriction_exact_sequence wikiPageWikiLinkText "inflation-restriction exact sequence".
- Inflation-restriction_exact_sequence wikiPageUsesTemplate Template:Algebra-stub.
- Inflation-restriction_exact_sequence wikiPageUsesTemplate Template:Cite_book.
- Inflation-restriction_exact_sequence wikiPageUsesTemplate Template:Reflist.
- Inflation-restriction_exact_sequence subject Category:Homological_algebra.
- Inflation-restriction_exact_sequence hypernym Sequence.
- Inflation-restriction_exact_sequence comment "In mathematics, the inflation-restriction exact sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the study of spectral sequences.Specifically, let G be a group, N a normal subgroup, and A an abelian group which is equipped with an action of G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G/N acts on AN = { a ∈ A : na = a for all n ∈ N}.".
- Inflation-restriction_exact_sequence label "Inflation-restriction exact sequence".
- Inflation-restriction_exact_sequence sameAs Q6030157.
- Inflation-restriction_exact_sequence sameAs m.0gk_mm_.
- Inflation-restriction_exact_sequence sameAs Q6030157.
- Inflation-restriction_exact_sequence wasDerivedFrom Inflation-restriction_exact_sequence?oldid=705929301.
- Inflation-restriction_exact_sequence isPrimaryTopicOf Inflation-restriction_exact_sequence.