Timeline for Inner products on abelian groups and general modules
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 31, 2017 at 21:50 | comment | added | Alex Shpilkin | @YCor Well, it could be that there is no unique general theory. I’m only trying to figure out if anyone actually cared enough to pose the question. | |
| Jan 31, 2017 at 21:40 | comment | added | Alex Shpilkin | @Kevin Thus (reference-request): I’m searching for a unified treatment of inner products on the different kinds of stuff one can apparently define them on, the choice of stuff being motivated by the “eating” of a meaningful set of theorems. (Re: choosing $\hat G \cong G$, yes, a general description of duality would be another way to put it—but I don’t know how to make it include the representation ring example. It is funny, though, how the $\hat G \cong G$ description automatically yields that the target of the product for finite groups is $\mathbf Z/e\mathbf Z$.) | |
| Jan 31, 2017 at 21:25 | comment | added | YCor | The choice of the target of the inner product is already not clear. Of course you can map into the base ring, but there are other natural choices (e.g, for a local ring, the injective hull of its residual field; in the case of $\mathbb{Z}$, $\mathbb{Q}/\mathbb{Z}$, etc). | |
| Jan 31, 2017 at 21:15 | comment | added | Kevin Buzzard | What do you actually want to know? If $G$ is abelian then an "inner product" on $G$ could just be thought of as an isomorphism from $G$ to its dual. But I don't really see a maths question here. You can make any definition you like but the proof of the pudding is in the eating (is that a UK expression??) | |
| Jan 31, 2017 at 21:14 | review | First posts | |||
| Jan 31, 2017 at 21:15 | |||||
| Jan 31, 2017 at 21:11 | history | asked | Alex Shpilkin | CC BY-SA 3.0 |