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Questions about the branch of algebra that deals with groups.

5 votes
Accepted

Properties of stabilizers of adjoint action general linear group

This is true and follows from: Claim: Let $x$ be a $n\times n$ matrix with $\mathbb{C}$-coefficients. Then the centralizer $C(x)$ of $x$ in $GL_n(\mathbb{C})$ fits into a short exact sequence $1\right …
Jef's user avatar
  • 984
12 votes
Accepted

Does $G_2(\mathbb{Z})$ depend on the choice of an integral model?

The short answer is no, because a Chevalley group has infinitely many $\mathbb{Z}$-points (even Zariski dense by the Borel density theorem). For the long answer, let me first completely describe all $ …
Jef's user avatar
  • 984