Timeline for Relative Frobenius Structure on the Category of G-modules
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 23, 2010 at 8:35 | comment | added | Hanno |
It's not clear to me why there has to exist a characteristic function on which the given map does not vanish. Further, what's the formal argument to show that there's no integer value $\sum_{k\in G/H} t(k)\cdot\delta_x$ could be sent to? (One could try to split off a large finite sum to see that it's value equals a large multiple of $\delta_x$'s value -- but this doesn't help, because the remaining sum/function could have an equally large value. Reminds me a bit of the proof that ${\mathbb Z}^{{\mathbb N}}$ is not free.)
|
|
| Jan 22, 2010 at 23:44 | comment | added | Ben Webster♦ | With your first comment, you're right that I made a mistake (fixed above), but it makes no difference to the argument. On the second point, I've tried to clarify. | |
| Jan 22, 2010 at 23:43 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
added 416 characters in body
|
| Jan 22, 2010 at 22:46 | comment | added | Hanno | Ben, yet another question: How do you know from the infinity of the G-orbits that the coinvariants are trivial? | |
| Jan 22, 2010 at 21:28 | comment | added | Hanno |
Thank you, Ben! One question concerning your identification of $\text{Hom}_H({\mathbb Z}G,{\mathbb Z}[G/H])$ with the ${\mathbb Z}$-valued functions on $G\times_H G/H$: In the former, the image of some element in $G$ has only finitely many nonzero coefficients in ${\mathbb Z}[G/H]$, whereas you impose no finiteness conditions on the functions on $G\times_H G/H$. How does this fit together?
|
|
| Jan 22, 2010 at 18:06 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
added 92 characters in body; deleted 9 characters in body
|
| Jan 22, 2010 at 17:47 | history | answered | Ben Webster♦ | CC BY-SA 2.5 |