Timeline for Calculation of the Schur multiplier of $\mathbb Z^2$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 27, 2018 at 7:29 | comment | added | Naren Manjunath | @QiaochuYuan Thanks. I didn't know the finiteness condition. I am trying to interpret 'central extension' as the group of symmetries on a two-dimensional lattice in the presence of a magnetic field (for a fixed field, the translation operators determine a projective representation of $\mathbb Z^2$). So different extensions would correspond to different magnetic fields, and I would not expect there to be a universal central extension for this problem. | |
| Jun 26, 2018 at 23:19 | comment | added | Qiaochu Yuan | People use "Schur multiplier" to refer to both $H_2(G, \mathbb{Z})$ and $H^2(G, \mathbb{C}^{\times})$ for $G$ a finite group because they are (noncanonically) isomorphic in that case, which they aren't in general. Also, the universal central extension is an extension of $G$ by $H_2(G, \mathbb{Z})$ and it only exists in general if $G$ is perfect, which $\mathbb{Z}^2$ isn't. | |
| Jun 26, 2018 at 11:10 | vote | accept | Naren Manjunath | ||
| Jun 26, 2018 at 8:54 | answer | added | Francesco Polizzi | timeline score: 7 | |
| Jun 26, 2018 at 8:03 | review | Close votes | |||
| Jun 26, 2018 at 9:30 | |||||
| Jun 26, 2018 at 7:28 | review | First posts | |||
| Jun 26, 2018 at 7:35 | |||||
| Jun 26, 2018 at 7:28 | history | asked | Naren Manjunath | CC BY-SA 4.0 |