Timeline for Existence of a Lie algebra element orthogonal to the adjoint orbit of another element
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2015 at 1:00 | comment | added | Francois Ziegler | Sounds like a control theory problem (à la this) that you might need to post as such... | |
| Apr 21, 2015 at 0:37 | comment | added | Benjamin | Here $a,b$ are some given elements of $\mathfrak{g}$ such that $\{a,b\}_{L.A.} = \mathfrak{g}$. | |
| Apr 21, 2015 at 0:29 | comment | added | Benjamin | I'm interested in finding a condition for the curve to have $\{g_t(A)\}$ spanning, so the curve is not given. The actual curves I'm interested in are solution to $\frac{d g_t}{dt} = (a + w(t)b)g_t$ for some smooth function $w(t)$. Ultimately I'm hoping for a condition on the function $w$. | |
| Apr 21, 2015 at 0:26 | comment | added | Francois Ziegler | If you are at liberty to draw the curve $\{g_t\}$ at will, then I sketched a way. If you already have the curve and need to decide whether $\{g_t(A)\}$ spans, we might need to know more on how your curve is given. | |
| Apr 21, 2015 at 0:09 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Apr 20, 2015 at 19:24 | comment | added | Benjamin | That's very clear thanks. Is there a criterion that can be deduced for which curves, or at least some non trivial curves, which $Ad_{g_t}(A)$ will fail to span the Lie algebra? In fact this issue only matters if $G$ is simple so that's the only case I care about. | |
| Apr 19, 2015 at 18:54 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Apr 19, 2015 at 13:48 | history | answered | Francois Ziegler | CC BY-SA 3.0 |