Timeline for Lie group operation and tangent vectors
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2011 at 6:00 | comment | added | Johannes Ebert | The equation $(\alpha\beta)'(0)=\lim_{t\to 0}\underbrace{\frac{\alpha(t)\beta(t)-e}{t}}$ does not make sense without additional information, because you cannot subtract. Either you embed the group in $GL_n$, or you pick a chart in which you can take differences, for example exponential charts. How the multiplication relates to addition in exponential charts is the CBH formula. | |
| Apr 25, 2011 at 11:06 | comment | added | darij grinberg | I don't believe we can use BCH here, as the proof of BCH (the geometric one) requires lots of assertions of the same kind (but harder) than the OP's question. | |
| Apr 25, 2011 at 11:01 | comment | added | darij grinberg | Ah, you mean distributivity. | |
| Apr 25, 2011 at 11:00 | comment | added | darij grinberg | Which "first equation"? | |
| Apr 25, 2011 at 10:58 | history | answered | Johannes Ebert | CC BY-SA 3.0 |