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Results tagged with group-cohomology
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user 9672
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.
3
votes
Accepted
symmetric measurable 2-cocycles on compact abelian groups vanish?
One way to see this is to note that $T$ splits from any locally compact abelian group (D.L. Armacost, The Structure of Locally Compact Abelian Groups, 6.16). If the cocycle is commutative, then the as …
- 5,654
5
votes
Extensions of topological groups
Bugs is right. If $G$ is locally compact abelian and multiplication by $2$ (or squaring) is an automorphism of $G$, then $H^2(G,U(1))$ is isomorphic to the group of alternating bi-characters $G\times …
- 5,654
1
vote
Equivalence of central extensions of Abelian groups
This generalizes to locally compact abelian (LCA) groups.
Suppose $G$ is a LCA group and you have a central extension
$0\to \mathbb T \to \tilde G\to G \to 0$
which admits a continuous section. The …
- 5,654
3
votes
The extension class of a finite Heisenberg group
I believe that your conjecture is equivalent to Theorem 3.5 in the paper Locally Compact Abelian Groups with Symplectic Self-duality, Advances in Mathematics, volume 225, pages 2429-2454, 2010.
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