New answers tagged algebraic-groups
2
votes
Algebraic path connecting specific elements in $\mathbf{GL}_{3}(\mathbb{Z})$
Lemma 3.13 in the article has the purpose to show that $(123)$ operates trivially on $T^{\otimes 3}$ with $T$ the cofiber of $\mathbb{G}_m^3 \longrightarrow \mathbb{A}^3$ which has the consequence ...
- 2,249
3
votes
Accepted
What is the meaning of $X^*(T)_{\mathbb Q}$ here?
$X^\ast(T_i)$ is an abelian group, and $X^\ast(T_i)_\mathbb{Q}$ is the tensor product $X^\ast(T_i) \otimes_\mathbb{Z} \mathbb{Q}$.
- 113
1
vote
Algebraic path connecting specific elements in $\mathbf{GL}_{3}(\mathbb{Z})$
After brute force calculation, I find out such an $\mathbf{A}(t)$:
$$
\begin{bmatrix}
-t^2+1 & t^4-3t^3+3t & 3t^2-3t\\
0 & -t^2+1 & t\\
t & 0 & -t^2+1
\end{...
- 61
4
votes
Algebraic path connecting specific elements in $\mathbf{GL}_{3}(\mathbb{Z})$
We don't want/require a map from the whole line, just some non-empty open subset. For example, set $g(t)=1-3t+3t^2$ and consider the open subset $U=D(g)$ inside $\mathbb A^1$. Then there is an ...
- 6,236
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