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Results tagged with group-cohomology
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user 121
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.
5
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0
answers
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Is there a composite-order generalization of the homomorphism on Rep(Z/p) giving total dimen...
Let $p$ be a prime, let $\mathbb{Z}_p$ be the ring of $p$-adic integers, and let $G$ be a cyclic group of order $p$. It is rather well-known that finite rank $\mathbb{Z}_p$-free representations of $G …
- 45.7k
29
votes
Accepted
$H^4$ of the Monster
There is some evidence from characters that $H^4(M,\mathbb{Z})$ contains $\mathbb{Z}/12\mathbb{Z}$. In particular, the conjugacy class 24J (made from certain elements of order 24) has a character of …
- 45.7k
7
votes
Classifying Space of a Group Extension
Your picture is essentially correct, except you need to specify that the maps take basepoints to basepoints (i.e., they are pointed maps).
BG is given as the homotopy fiber of a pointed map from B(G/ …
- 45.7k
4
votes
Accepted
Relationship between irreducible representations of the Schur covering group and elements of...
The answer to your question is Yes. Consider your covering group $C$ as a central extension:
$$1 \to N \to C \to G \to 1$$
and suppose it is given by a 2-cocycle $\alpha \in H^2(G, N)$. Then for any …
- 45.7k
7
votes
Tate Cohomology via stable categories
Google gives the following paper: Greenlees, Tate cohomology in axiomatic stable homotopy theory. It gives a definition of the Tate construction using Bousfield localization and completion, and has s …
- 45.7k