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Results tagged with gr.group-theory
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user 136187
Questions about the branch of algebra that deals with groups.
8
votes
0
answers
244
views
When does a semisimple $\mathbb{C}$-algebra come from a group?
Let $\mathcal{A}$ be a semisimple $\mathbb{C}$-algebra. By the Artin-Wedderburn theorem, it is isomorphic to a direct product of matrix algebras:
$$ \mathcal{A} = \prod_{i=1}^m M_{n_i}(\mathbb{C})$$
U …
- 297
4
votes
1
answer
404
views
Finitely Additive Homogeneous Translation Invariant Measure on $\mathcal{P}(\mathbb{R})$
It is known that there exists a finitely additive translation invariant measure on $\mathbb{R}$ that extends the Lebesgue measure. I.e. a function $m:\mathcal{P}(\mathbb{R}) \rightarrow [0,\infty]$ th …
- 297
4
votes
1
answer
289
views
Residual finiteness of random groups with property (T)
A well known result of A. Zuk states that for $\frac{1}{3} < d < \frac{1}{2}$, a random group $\Gamma$ with respect to Gromov's density model with density $d$ has Kazhdan's property (T) with overwhelm …
- 297