All Questions
Tagged with rt.representation-theory solvable-groups
3 questions
23
votes
2
answers
967
views
Solvable groups that are linear over $\mathbb{C}$ but not over $\mathbb{Q}$?
Let $\Gamma$ be a finitely generated finitely presented virtually solvable group. Assume that there exists an injective representation $\Gamma \to \operatorname{GL}_n(\mathbb{C})$. Is it true that ...
- 1,170
3
votes
1
answer
176
views
Example of a supersolvable Lie group/algebra whose nilradical does not have a complement
What is an example of a real solvable simply-connected Lie group $G$ whose nilradical does not have a complement (that is, $G$ is not a semidirect product of the nilradical and another subgroup)? Is ...
- 33
1
vote
0
answers
172
views
Is every connected solvable group Borel?
Is every connected solvable algebraic group a Borel subgroup of a reductive group? If a counterexample exists, I would ideally like it to be over $\Bbb C$.
- 3,079