Timeline for Minimal dimension of a Lie algebra of matrices, with a restrictive property
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2015 at 19:19 | history | edited | Dave Witte Morris | CC BY-SA 3.0 |
proof of the reducible case was much more complicated than necessary
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| Mar 30, 2015 at 18:10 | comment | added | Dave Witte Morris | The proof in the first paragraph shows that $n-1$ is not sharp unless $n$ is very small. This is because $\dim \mathfrak{g} = \dim (\mathfrak{b} \cap \mathfrak{b}^-) + 2 \dim (\mathfrak{g}/\mathfrak{b})$ is larger than $1 + 2 \dim (\mathfrak{g}/\mathfrak{b})$ unless $\mathfrak{g} = \mathfrak{sl}_2(\mathbb{C})$ (so $\dim \mathfrak{g} = 3$). | |
| Mar 30, 2015 at 18:03 | history | edited | Dave Witte Morris | CC BY-SA 3.0 |
correction: need an opposite Borel subalgebra to apply to y
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| Mar 30, 2015 at 17:37 | history | edited | Dave Witte Morris | CC BY-SA 3.0 |
corrected a typo and removed an ambiguity
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| Mar 30, 2015 at 17:31 | history | answered | Dave Witte Morris | CC BY-SA 3.0 |