Timeline for Does Maurer-Cartan form define surjection from Lie Group to Algebra-valued forms?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jan 14, 2017 at 15:42 | vote | accept | Okazaki | ||
| Jan 14, 2017 at 15:36 | comment | added | Ben McKay | Moreover, under right translation, the Maurer--Cartan form always remains a linear isomorphism of each tangent space to the Lie algebra, so many $\mathfrak{g}$-valued 1-forms do not appear in this way. | |
| Jan 14, 2017 at 15:32 | comment | added | Ben McKay | If you left translate them to identify different tangent spaces of $G$, you always get the same 1-form, by left invariance, so the answer is no. If you right translate, you get 1-forms varying in the adjoint representation, but you never get the zero 1-form, so then the answer is no. | |
| Jan 14, 2017 at 15:31 | history | answered | Ben McKay | CC BY-SA 3.0 |