3
votes
2answers
286 views

Infinitesimal rigidity vs. local rigidity

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup. This question talked about the difference of ...
2
votes
2answers
277 views

Infinitesimal deformations of a discrete group inside Lie groups vs. algebraic groups

Let $G$ be an algebraic group with Lie algebra $\mathfrak g$ and let $\Gamma$ be any finitely generated (discrete) group. One can consider the representation variety $\mathfrak ...
12
votes
1answer
565 views

Lie groups vs. algebraic groups and deformations

I am interested in deformations of (discrete subgroups of) Lie groups. But, as I understand it, deformation theory, as a theory, prefers to speak schemes. At least the classical Lie groups can be ...
6
votes
1answer
243 views

Words in two infinitismal rotations

I asked this as subquestion in a comment pursuant to my Banach-Tarski question. I think it is worth promoting here to a question in its own right. Consider these two matrices over ${\Bbb ...