Timeline for Can Hom_gp(G,H) fail to be representable for affine algebraic groups?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 23, 2022 at 11:08 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Dec 23, 2022 at 10:42 | comment | added | David E Speyer | @Vincent Sorry for introducing more confusion. I did, indeed, want $n$ nilpotent. | |
| Dec 23, 2022 at 10:41 | history | edited | David E Speyer | CC BY-SA 4.0 |
edited body
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| Dec 23, 2022 at 9:14 | comment | added | Vincent | It seems to me that the original formulation was the right one and the edit introduced an error. But then again I know virtually nothing about this subject, so it seems likely that I am wrong. Either way I would be happy if someone could clarify this | |
| Dec 23, 2022 at 9:07 | comment | added | Vincent | I am confused now about the $x$ nilpotent vs $n$ nilpotent business. The way it is written now in the post it looks like the homomorphism is very picky and only accepts nilpotent elements as input. But that is not how homormorphisms are supposed to work, right? The domain should be the whole group | |
| Dec 23, 2022 at 4:16 | comment | added | LSpice | @YCor, ah, you are right. I thought the $n$ in $f_i = n^i/i!$ was an integer; it didn't occur to me that it was a ring element. | |
| Dec 23, 2022 at 3:13 | comment | added | YCor | @LSpice No, I think "$n$ is nilpotent" is correct. You have a unital ring homomorphism $R[y,y^{-1}]\to R[x]$, mapping $y$ to an element $\sum_{i\ge 0}f_ix^i$; this element must be inversible and this is equivalent to: $f_0$ is inversible in $R$ and $f_i$ is nilpotent for all $i\ge 1$. (Then the condition of being a Hopf algebra homomorphism implies the given formula, namely $f_i=f_1^i/i!$, with $f_1$ nilpotent.) | |
| Dec 23, 2022 at 1:35 | history | edited | David E Speyer | CC BY-SA 4.0 |
deleted 5 characters in body
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| Dec 22, 2022 at 23:03 | comment | added | LSpice | "n must by nilpotent" → "$x$ must be nilpotent", I think. | |
| S Jan 11, 2021 at 11:54 | history | suggested | Captain Lama | CC BY-SA 4.0 |
Put all the Hom, Spec, and G in TeX format.
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| Jan 11, 2021 at 10:57 | review | Suggested edits | |||
| S Jan 11, 2021 at 11:54 | |||||
| S Apr 30, 2019 at 16:55 | history | suggested | display llvll | CC BY-SA 4.0 |
just added some dollars
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| Apr 30, 2019 at 16:46 | review | Suggested edits | |||
| S Apr 30, 2019 at 16:55 | |||||
| Nov 12, 2017 at 22:12 | comment | added | Qiaochu Yuan | "Characteristic zero" here should be interpreted to mean "$\mathbb{Q}$-algebra," I guess. | |
| Nov 4, 2009 at 17:30 | vote | accept | David Zureick-Brown | ||
| Nov 4, 2009 at 15:58 | history | answered | David E Speyer | CC BY-SA 2.5 |