View Single Post
Mar28-12, 03:14 PM
P: 3,221
I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry.
If [itex]\mathcal{D}_1, \mathcal{D}_2[/itex] are (natural) graded derivations of degrees [itex]r_1,r_2[/itex] respectively, then the operator:
[itex][\mathcal{D}_1,\mathcal{D}_2] := \mathcal{D}_1 \circ \mathcal{D}_2 - (-1)^{r_1 r_2} \mathcal{D}_2 \circ \mathcal{D}_1[/itex]

is a natural graded derivation of degree [itex]r_1+r_2[/itex].
I am finding it difficult to prove property 2 and 3 of graded derivation for this bracket.
Property 2 is given in the next page in definition 1.

I am uploading scans of my work (hopefully my hand written work won't stir you away).
Attached Thumbnails
Graded1.jpg   Graded2.jpg   Graded3.jpg  
Phys.Org News Partner Science news on
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice