Timeline for Definition of a Grothendieck ring
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2011 at 10:09 | vote | accept | Peadar Coyle | ||
| Sep 4, 2011 at 0:35 | answer | added | Donu Arapura | timeline score: 16 | |
| Sep 3, 2011 at 15:08 | comment | added | Donu Arapura | Yes, it's the same as what I was thinking. Another example, perhaps closer to what you want, is the category of complex reps of compact Lie group (e.g. finite group). This a tensor category. Every object is determined up to iso. by its character $\chi_V$. Note $\chi_{V\oplus W}=\chi_V+\chi_W$ and $\chi_{V\otimes W}=\chi_V\chi_W$ which are the same relations as in the Grothendieck ring. So perhaps you can view the Groth. ring as a generalization of character theory. I'm sure someone will write more. | |
| Sep 3, 2011 at 14:39 | history | edited | Peadar Coyle | CC BY-SA 3.0 |
Refined the question
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| Sep 3, 2011 at 14:37 | comment | added | Peadar Coyle | I'm referring to the Grothendieck Ring in Tensor Categories. I'm not sure if this is the same.... | |
| Sep 3, 2011 at 13:54 | answer | added | Johan Öinert | timeline score: 7 | |
| Sep 3, 2011 at 12:11 | comment | added | Todd Trimble | Also, I think the question is ambiguous, because there's more than one sense in which people use the term "Grothendieck ring". | |
| Sep 3, 2011 at 12:09 | comment | added | Donu Arapura | I agree with quid's comment, but I'll make an attempt anyway. The first example you should contemplate is the Grothendieck ring of finite dimensional vector spaces. You have a symbol for each isomorphism class of spaces. Adding symbols corresponds to direct sum, and multiplying to tensor products. It seems a bit like the dimension doesn't it? | |
| Sep 3, 2011 at 11:53 | comment | added | user9072 | Perhaps you could mention those at which you looked already: so that noone suggests those, and it is easier to infer what would be 'good'. | |
| Sep 3, 2011 at 11:47 | history | asked | Peadar Coyle | CC BY-SA 3.0 |