Timeline for Representation of Lie algebra $\operatorname{SE}(2)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2021 at 13:47 | comment | added | Ben McKay | @Vichakh: the idea is that every rigid motion of the plane is a diffeomorphism of the plane, so the group $SE(2)$ of orientation preserving rigid motions of the plane is a group of diffeomorphisms of the plane. So Chik67 is suggesting that the map $R$ is the inclusion map. But he is wrong, that is the map $\mathcal{A}$. The map $R$ is the action now indicated in the question. | |
| Aug 17, 2021 at 11:49 | comment | added | Chivul | Can you explain more about the map $R:\operatorname{SE}(2)\rightarrow \operatorname{Diff}(\mathbb{R}^2)$? I have not yet caught up with the idea. | |
| Aug 17, 2021 at 9:19 | comment | added | Ben McKay | No, the representation is not a map to diffeomorphisms. Every representation is a morphism to linear transformations of some vector space. In this problem, the vector space is a space of square integrable functions, as you seen in the paper which the OP references in his question. | |
| Aug 17, 2021 at 4:40 | review | First posts | |||
| Aug 17, 2021 at 5:19 | |||||
| Aug 17, 2021 at 4:37 | history | answered | Chik67 | CC BY-SA 4.0 |