Timeline for Semisimple Lie groups admitting a free algebra of invariants
Current License: CC BY-SA 3.0
9 events
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| Mar 30, 2018 at 14:01 | comment | added | Paul Levy | This question is slightly confusing - it took me some time to track down the passage in Algebraic Geometry IV which says that "the connected ... admitting ... have not yet been determined". The point is that any semisimple algebraic group admits at least one representation for which the invariants are free: the adjoint representation. When Popov & Vinberg talk about "connected semisimple linear groups satisfying (FA)" they mean: pairs $(G,V)$ where $G$ is semisimple and $V$ is a representation. So the question really is, for a fixed $G$, what is the number $\geq 1$ of such representations? | |
| Mar 20, 2018 at 20:34 | comment | added | svelaz | @JimHumphreys thank you very much. I chose the tag "Lie groups" because the question is very close to "which are the semisimple lie group actions with an affine space as a quotient" | |
| Mar 20, 2018 at 20:30 | history | edited | svelaz | CC BY-SA 3.0 |
added 93 characters in body
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| Mar 20, 2018 at 20:07 | comment | added | Jim Humphreys | P.S. Here is the link to the Russian original: mathnet.ru/php/… | |
| Mar 19, 2018 at 0:37 | comment | added | Jim Humphreys | As far as I know, there is no further progress on the classification; this doesn't answer your question, however. I'd suggest you provide more explicit references, e.g., to Popov's paper, which I guess is this one: mathscinet.ams.org/mathscinet-getitem?mr=651651 (it's freely available online in Russian but not English). Also, Lie group theory probably has little to do with the question asked. Anyway, the connected semisimple Lie groups coincide with the connected semisimple algebraic groups over an algebraically closed field of characteristic 0 (Chevalley). | |
| Mar 16, 2018 at 20:34 | history | edited | Mikhail Borovoi |
two tags added
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| Mar 16, 2018 at 17:53 | history | edited | Martin Sleziak |
Removed deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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| Mar 16, 2018 at 17:46 | history | migrated | from math.stackexchange.com (revisions) | ||
| Mar 16, 2018 at 16:33 | history | asked | svelaz | CC BY-SA 3.0 |