Timeline for Infinite dimensional simple algebras
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2017 at 4:20 | history | edited | Victor Protsak | CC BY-SA 3.0 |
rewrote adding localization and more details on the Lie algebra case
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| Apr 5, 2017 at 7:28 | comment | added | Victor Protsak | I have added some technical details. I am still unconvinced that this adds clarity for anyone unfamiliar with representation theory of semisimple Lie algebras (and primitive ideals). | |
| Apr 5, 2017 at 7:26 | history | edited | Victor Protsak | CC BY-SA 3.0 |
more details
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| Apr 5, 2017 at 2:57 | comment | added | Victor Protsak | This a well-developed theory, and it is not clear to me how much to say before it becomes too much (primarily, because the question itself is overly broad). As the first example, the annihilator of the Verma module with maximally non-integral infinitesimal character (generated by the corresponding maximal ideal of the center) works. I will add more refs when I have time. The fact that ideals of universal enveloping algebras are finitely generated is standard and follows from the fact that the associated graded algebra is Noetherian. In a way, the best clarification is "read the literature". | |
| Apr 4, 2017 at 23:34 | comment | added | Konstantinos Kanakoglou | I was wondering exactly the same thing. I think that mentioning a concrete example of a maximal ideal of infinite codimension, inside the UEA of some semisimple Lie algebra would clarify things. Also, mentioning the quotient and demonstrating that it is simple and fp, would add value to both the answer and the question as well. | |
| Apr 4, 2017 at 22:16 | comment | added | YCor | Why do maximal ideals of infinite codimension exist, and why is the quotient finitely presented? | |
| Apr 4, 2017 at 16:22 | history | edited | Victor Protsak | CC BY-SA 3.0 |
Expanded (matrix rings)
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| Apr 4, 2017 at 16:09 | history | answered | Victor Protsak | CC BY-SA 3.0 |