Timeline for Central extensions of SL2(R) by U(1) ?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2015 at 14:56 | comment | added | Jim Humphreys | Just a technical comment that you should use LaTeX for mathematical symbols, to avoid ambiguity. For instance, your symbol R might just mean a ring in the context of algebraic K-theory, or might mean the field $\mathbb{R}$ of real numbers. | |
| Feb 11, 2015 at 13:43 | comment | added | abx | If you are considering $\mathrm{SL}_2(\mathbb{R})$ as a discrete group, the answer is rather complicated, see this question and the various answers. On the other hand if you are considering $\mathrm{SL}_2(\mathbb{R})$ as a Lie group, then any central extension is the pushforward of the universal cover by some homomorphism $\mathbb{Z}\rightarrow \mathrm{U}(1)$; this follows easily from the fact that every central extension of $\mathfrak{sl}_2(\mathbb{R})$ is trivial. | |
| Feb 11, 2015 at 6:06 | history | asked | ShuklaS | CC BY-SA 3.0 |