Timeline for Representations are determined by characters : Groups and Lie algebras
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2020 at 18:56 | comment | added | Balazs Elek | A good reference is Humphrey's book "Representations of semisimple Lie algebras in the BGG category $\mathcal{O}$", see chapter 3 for extensions. | |
| Jan 8, 2020 at 9:49 | comment | added | Bugs Bunny | What are "these"? | |
| Jan 6, 2020 at 18:12 | comment | added | GA316 | Thank you. Can you suggest some references regarding these? | |
| Jan 6, 2020 at 12:11 | comment | added | Bugs Bunny | @Aaron Exactically, Aaron explained it well. A character is always a homomorphism from the Grothenideck group to some other group. Since $M^\prime$ and $M\oplus N$ give the same element of the Grothendieck group, they cannot be distinguished by a character... | |
| Jan 6, 2020 at 8:17 | comment | added | Aaron | @GA316 In this context, I believe it means a short exact sequence of the form $0\to M\to M'\to N\to 0$ With a split short exact sequence, $M'\cong M\oplus N$, but if you do not have complete reducibility, then there will exist non-split short exact sequences. | |
| Jan 6, 2020 at 7:51 | comment | added | GA316 | Thanks. can you please tell me what is the meaning of extensions? | |
| Jan 3, 2020 at 16:52 | history | answered | Bugs Bunny | CC BY-SA 4.0 |