Timeline for A tri-grading on the de Rham complex of a Lie group?
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Nov 17, 2020 at 22:37 | comment | added | YCor | This is a grading in $\mathbf{Z}$, namely $\mathfrak{g}_{-1}\oplus\mathfrak{g}_0\oplus\mathfrak{g}_1$. On the Chevalley-Eilenberg complex this yields a $\mathbf{N}\times\mathbf{Z}$-grading, for which the differential shifts the grading by $(1,0)$ (or $(-1,0)$ in homology), and the homology inherits a $\mathbf{N}\times\mathbf{Z}$-grading. | |
| Nov 17, 2020 at 20:37 | comment | added | Bertram Arnold | The decomposition only exists after tensoring with $\mathbb C$ and is not preserved by the differential - the annihilator of a subbundle generates a differential subalgebra iff sections of the subbundle are closed under Lie bracket. | |
| Nov 17, 2020 at 20:21 | history | asked | Dick Johnson | CC BY-SA 4.0 |