Timeline for Difference between $\mathfrak{g}/\!/G$ and $G/\!/G$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2022 at 21:00 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Aug 4, 2022 at 14:13 | comment | added | skd | At least if $G$ is reductive (over $\mathbf{C}$), the isomorphism between the completions of $\mathfrak{g}/\!\!/G$ and $G/\!\!/G$ can be viewed as a manifestation of the Chern character from complex K-theory of $BG$ tensored with $\mathbf{C}$ to the 2-periodified $\mathbf{C}$-cohomology of $BG$. Note that if $G$ is simply-connnected, $BG$ is not homotopy equivalent to a finite CW-complex (but it is an increasing union of such), so the completions really are necessary. | |
| Aug 4, 2022 at 13:46 | comment | added | Friedrich Knop | @LSpice Right, should be characteristic zero. | |
| Aug 4, 2022 at 13:22 | history | edited | LSpice | CC BY-SA 4.0 |
Link to ~sceptical chymist~ skeptical comment
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| Aug 4, 2022 at 13:22 | comment | added | LSpice | @FriedrichKnop, re, for reductive groups in characteristic 0 (which I agree is what we seem to be discussing!), right? | |
| Aug 4, 2022 at 13:05 | history | edited | David E Speyer | CC BY-SA 4.0 |
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| Aug 4, 2022 at 12:20 | comment | added | Friedrich Knop | I am very skeptical that for arbitrary groups completion commutes with taking invariants. Is there a reference? For reductive groups it follows easily from complete reducibility. | |
| Aug 4, 2022 at 11:49 | history | edited | LSpice | CC BY-SA 4.0 |
Link to answer and comments
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| Aug 4, 2022 at 11:42 | history | answered | David E Speyer | CC BY-SA 4.0 |