Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with group-cohomology
Search options not deleted
user 4008
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
16
votes
Accepted
Where can I easily look up / calculate (abelian) group cohomology?
This group is best understood in terms of the universal coefficient formula,
i.e., in terms of the homology of the involved group. Hence, if $A$ is any
abelian group we have $H_1(A)=A$ and the additio …
- 22.6k
14
votes
Accepted
Injection of Ext into H^2
You get a description from the universal coefficient theorem which gives a (split) exact sequence
$$
0\to \mathrm{Ext}(H_1(G),A) \to H^2(G,A) \to \mathrm{Hom}(H_2(G),A) \to 0
$$
and the fact that $H_1 …
- 22.6k
19
votes
Accepted
Hilbert 90 for algebras
It's actually easier to go the other way around. Finite dimensional modules over
an algebra $A$ fulfils the Krull-Remak-Schmidt theorem of being isomorphic to a
direct sum of indecomposable modules wi …
- 22.6k
2
votes
How to fit res map into a long exact sequence?
There is a long exact sequence but I think it is largely useless: We have that for any $H$-module $B$ the cohomology $H^n(H,B)$ is equal to the cohomology $H^n(G,B^G_H)$ of the induced module $B^G_H$. …
- 22.6k