Timeline for Simplest explicit counterexample for $Vect(BG) \ne Rep(G)$ as monoids
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 10, 2016 at 17:48 | comment | added | Saal Hardali | @QiaochuYuan Thanks! Your answer is great. I've accepted Niel's answer since it was closer to the example I wanted (although my initial phrasing wasn't so accurate). | |
| May 9, 2016 at 22:11 | comment | added | Chris Schommer-Pries | I think the question should really be about compact Lie groups. You can get another easy counter example with $G = \mathbb{R}$, where $BG$ is contractible. | |
| May 9, 2016 at 21:30 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| May 9, 2016 at 21:30 | comment | added | Qiaochu Yuan | @Yonatan: sorry, I had in mind unitary representations. In any case $SL_2(\mathbb{R})$ has no nontrivial $1$-dimensional representations. | |
| May 9, 2016 at 20:34 | comment | added | Yonatan Harpaz | Isn't the inclusion $SL_2(\mathbb{R}) \to GL_2(\mathbb{C})$ a non-trivial finite-dimensional complex representation? | |
| May 9, 2016 at 20:20 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |