Timeline for Lie algebra elements commuting with a principal nilpotent element
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2019 at 14:39 | comment | added | YCor | I completed the work, removing the new question from the old post and adding links between the questions. | |
| Jul 17, 2019 at 14:37 | history | edited | YCor | CC BY-SA 4.0 |
reverted to previous version (since new question now in separate post). Added follow-up
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| Jul 17, 2019 at 13:43 | comment | added | AThomas | @YCor: Ok, I will do that. | |
| Jul 17, 2019 at 11:36 | comment | added | YCor | It is usually not considered fair on this site to modify the question after somebody bothered to post an answer (at least if this answer is not completely trivial and rather worth a comment). I'd recommend you post your modified version as a separate question. | |
| Jul 17, 2019 at 10:01 | history | edited | AThomas | CC BY-SA 4.0 |
added 321 characters in body
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| Jul 17, 2019 at 9:54 | comment | added | AThomas | @LSpice: Yes, they are more usually called regular nilpotent. Ginzburg also calls them principal nilpotent. | |
| Jul 16, 2019 at 19:38 | comment | added | LSpice | As I take @YCor's comment to be indicating, I'm pretty sure that when you refer to "the set of all polynomials $P$ applied to $r(A)$ such that …" and "the space $P \in \mathbb C[x]$ with …", you mean "the set of all values $P(r(A))$ such that …" and "the space of $P(r(A))$ with $P \in \mathbb C[x]$ and …" (that is, that the elements are values of polynomials, not the polynomials themselves—as matters when computing dimension!). | |
| Jul 16, 2019 at 18:55 | comment | added | LSpice | I think such elements are usually called regular, not principal. | |
| Jul 16, 2019 at 18:34 | answer | added | YCor | timeline score: 5 | |
| Jul 16, 2019 at 17:45 | comment | added | YCor | "the space $P \in \mathbb{C}[x]$ with $P(r(A)) \in r(\mathfrak{g})$" can concisely be written as $\mathbf{C}[r(A)]\cap r(\mathfrak{g})$. | |
| Jul 16, 2019 at 16:03 | history | asked | AThomas | CC BY-SA 4.0 |