Timeline for What is the intersection of all maximal abelian subalgebras of a compact simple Lie algebra, containing a given element?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 27, 2022 at 20:54 | comment | added | Fridrich Valach | @Echo Great, thanks! | |
| May 25, 2022 at 17:46 | comment | added | user473423 | Humphries book on Lie algebras, for instance. A good survey is in the first chapters of Knapp's book on representation theory of semisimple Lie groups. | |
| May 24, 2022 at 17:38 | comment | added | Fridrich Valach | @YCor Thanks for the explicit results! | |
| May 24, 2022 at 17:28 | comment | added | Fridrich Valach | @Echo where can one learn more about this? | |
| May 24, 2022 at 12:47 | comment | added | YCor | In $\mathfrak{so}(n)$, these are if I'm correct, those elements of $\mathfrak{so}(n)$ that are proportional to $x$ on each generalized eigenspace of $x$ (i.e. $\mathrm{Ker}(x)$ or $\mathrm{Ker}(x^2+s)$ for $s>0$), except precisely, when $ K_x=\mathrm{Ker}(x)$ is 2-dimensional (happens only when $n$ is even), in which case the element is allowed to be arbitrary on the 2-plane $K_x$. Here "proportional to 0" means "equal to 0". | |
| May 24, 2022 at 11:36 | history | edited | Fridrich Valach | CC BY-SA 4.0 |
added 257 characters in body
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| May 20, 2022 at 14:28 | comment | added | user473423 | It depends on the level of regularity of the element. Generally speaking, it is the algebra generated by the lowest dimensional face of a Weyl chamber, the element sits in. | |
| May 20, 2022 at 7:32 | comment | added | YCor | In $\mathfrak{su}(n)$ for a diagonal matrix $(a_1,\dots,a_n)$ these are the diagonal matrices $(d_1,\dots,d_n)$ in $\mathfrak{su}(n)$ such that $a_i=a_j$ implies $d_i=d_j$. | |
| May 20, 2022 at 6:19 | comment | added | Friedrich Knop | It's the center of the centralizer. | |
| May 20, 2022 at 0:11 | comment | added | Andrea Marino | Some examples and heuristics? | |
| May 19, 2022 at 23:57 | review | Close votes | |||
| May 20, 2022 at 1:16 | |||||
| S May 19, 2022 at 17:56 | review | First questions | |||
| May 19, 2022 at 19:07 | |||||
| S May 19, 2022 at 17:56 | history | asked | Fridrich Valach | CC BY-SA 4.0 |