Questions tagged [group-homology]
The group-homology tag has no usage guidance.
7
questions with no upvoted or accepted answers
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Group homology $\mathrm{SL}_2$ acting on $\mathrm{Sym}^g$
Let $k$ be a field. We write $\mathrm{Sym}^g(k^2)$ for the $g$-th symmetric power of the (a?) standard representation of $\mathrm{GL}_2(k)$ ($g\geq 0$ an integer). Here I consider $\mathrm{Sym}^g(k^2)$...
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Localizations of group algebras of free groups
$\newcommand{\QQ}{\Bbb Q}$
Let $G$ be a free group on the symbols $x_1, \dots, x_n$, with $\QQ[G]$ its rational group algebra.
Write $\varepsilon: \QQ[G] \to \QQ$ for the augmentation, and for $\...
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Is the Tensor/Exterior square $G\otimes G$ or $G\wedge G$ of infinite p-group also a p-group?
Let $G$ be an infinite countable p-group. Is it true that $G\otimes G$ or $G\wedge G$ are also p-groups? (where G acts on itself by conjugation). For simplicity, you can consider that $G=[G,G]$, and ...
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Methods for showing homology of a subgroup survives to the larger group
Suppose we have an inclusion of groups $G_1<G_2$. I am curious about what methods there are out there for analyzing the map $H_k(G_1;\mathbb Q)\to H_k(G_2;\mathbb Q)$. In particular, what are tools ...
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Reference request: Lower group (co)homology of linear groups
I am finding references about the following general question:
What is the group (co)homology $H_{i}(G,\mathbb{Z})$ for a linear group $G$?
In my case, I'm particularly interested in the special case ...
- 233
2
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Homology of linear groups over integral domains and their field of fractions
Let $A$ be a noetherian integral domain of finite Krull dimension with the field of fractions of $F$. Consider the natural injections $i_n:GL_n(A)\hookrightarrow GL_{n+1}(A)$, $j_n:GL_n(F)\...
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Explicit transgression maps for Group homology in LHS
This question is related to another question of mine (Here: Lyndon-Hochschild-Serre spectral sequence and cup products).
I'm trying to figure out if some diagram commutes an one of the maps involved ...
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