All Questions
Tagged with nonabelian-cohomology group-cohomology
9 questions
19
votes
3
answers
2k
views
Second nonabelian group cohomology: cocycles vs. gerbes
In 1965 Jean Giraud published two Comptes Rendus notes titled "Cohomologie non abélienne", and in 1971 he published a book with the same title.
In 1966 Tonny A. Springer's paper "Nonabelian $H^2$ in ...
- 14.2k
18
votes
2
answers
592
views
primary decomposition for nonabelian cohomology of finite groups
Let $G$ be a finite group, and let $M$ be a group on which $G$ acts (via a homomorphism $G\to \operatorname{Aut}(M)$).
If $M$ is abelian, hence a $\mathbb{Z}G$-module, there is a primary ...
- 35.9k
12
votes
0
answers
272
views
sequences in non-abelian group cohomology
In general, if we have a (pro-)finite group $G$ and a sequence of (continuous) non-abelian $G$-modules $$1\rightarrow A\rightarrow B\rightarrow C\rightarrow 0,$$ such that the image of $A$ lies in the ...
- 273
7
votes
2
answers
997
views
Non-abelian Ext functor and non-abelian $H^2$
Let $G$ be a group and
$$0\rightarrow K\rightarrow M\rightarrow N\rightarrow 0$$
a short exact sequence of groups. Now these are abelian groups, if I want to show that $\text{Hom}(G,M)\rightarrow \...
- 4,418
7
votes
0
answers
303
views
Albrecht Fröhlich's text `Groupoids, groupoid spaces and cohomology' (1965)
I am looking for Albrecht Fröhlich's unpublished text `Groupoids, groupoid spaces and cohomology' (1965). In this text Fröhlich defines cohomology of a group with coefficients in a groupoid (this was ...
- 14.2k
6
votes
1
answer
300
views
Connection between the classifications of group extensions and group-graded algebras in terms of non-abelian cohomology
First, consider group extensions with non-abelian kernel
$$1\to K\to G \to Q \to 1$$
It is well-known that these are classified by certain cohomological objects, specifically: Any such extension ...
- 9,650
3
votes
0
answers
308
views
Non-abelian group cohomology, additional information
Let $G$ be a (profinite) group, and let $M$ be a non-abelian $G$-module.
We know how to construct reasonably $H^0(G,M)$ and $H^1(G,M)$ and it turns out that $H^1(G,M)$ is just a pointed set and not ...
- 463
2
votes
1
answer
439
views
Minimal parabolic subgroups are $G(k)$-conjugate: a cohomological interpretation?
Let $G$ be a connected,reductive group over a $p$-adic field $k$. Let $M_0$ be a minimal Levi subgroup of $G$, and define $M_0^{\operatorname{der}}$ to be $M_0 \cap G_{\operatorname{der}}$. Lemma 2....
- 6,180
1
vote
0
answers
42
views
When is $B^G\backslash(B/A)^G$ finite?
Let $G$ be a locally compact group, let $A,B$ be (not necessarily abelian) connected reductive complex groups equipped with continuous actions of $G$ via algebraic automorphisms. Let $\phi:A\to B$ be ...
- 387