Timeline for Derivative of the projection map $\pi: G \times \mathfrak{g} \rightarrow G \times_K \mathfrak{g}$
Current License: CC BY-SA 4.0
4 events
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| Feb 24, 2022 at 2:25 | comment | added | Mira | @LSpice, I used the fact that $G \times_K \mathfrak{g} \rightarrow G/K$ is locally a trivial fibre bundle with fibre $\mathfrak{g}$ and since the quotient $G \times_K \mathfrak{g}$ is the associated bundle to the principal bundle $G \rightarrow G/K$, then the tangent space will split to be isomorphic to the vector space direct sum $\mathfrak{g}/\mathfrak{k}\oplus \mathfrak{g}$. | |
| Feb 24, 2022 at 2:09 | comment | added | LSpice | How do you identify $T_{\pi(g, X)}(G \times_K \mathfrak g)$ with $\mathfrak g/\mathfrak t \oplus \mathfrak g$? | |
| Feb 24, 2022 at 0:42 | history | edited | Mira | CC BY-SA 4.0 |
edited title
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| Feb 24, 2022 at 0:36 | history | asked | Mira | CC BY-SA 4.0 |