Timeline for Generating a reductive real Lie group with finitely many maximal real tori
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2012 at 18:16 | comment | added | Jeffrey Adams | You also need $\mathbb C^*$ factors | |
| Jan 25, 2012 at 13:52 | answer | added | Hugo Chapdelaine | timeline score: 1 | |
| Jan 25, 2012 at 13:45 | vote | accept | Hugo Chapdelaine | ||
| Jan 24, 2012 at 21:51 | history | edited | Hugo Chapdelaine |
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| Jan 24, 2012 at 21:39 | answer | added | Jim Humphreys | timeline score: 1 | |
| Jan 24, 2012 at 21:22 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Jan 24, 2012 at 20:52 | answer | added | algori | timeline score: 5 | |
| Jan 24, 2012 at 19:25 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Jan 24, 2012 at 19:25 | comment | added | Hugo Chapdelaine | So my maximal $\mathbf{R}$-tori will look like $(\mathbf{R}^{\times})^n\times (S^1)^m$ where $S^1$ stands for the unit circle. May be also I should have restricted my question to real algebraic reductive group | |
| Jan 24, 2012 at 19:22 | comment | added | Hugo Chapdelaine | By an $\mathbf{R}$-torus I mean the $\mathbf{R}$-valued points of an algebraic group $H$ defined over $\mathbf{R}$ such that $H\otimes_{\mathbf{R}}\mathbf{C}\simeq (\mathbb{G}_m/\mathbf{C})^n$. So for example, with a rank $1$ torus (case $n=1$), if $T$ is split then $H(\mathbf{R})\simeq \mathbf{R}^{\times}$ and if it is non-split (and non-empty) it is isomorphic to $SO(2)$. | |
| Jan 24, 2012 at 19:10 | comment | added | algori | Hugo -- what kind of tori do you have in mind? I.e., do you mean compact tori or products of $\mathbb{R}^*$'s or something else? | |
| Jan 24, 2012 at 18:54 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Jan 24, 2012 at 18:30 | history | asked | Hugo Chapdelaine | CC BY-SA 3.0 |