I want to prove the next assertion in Jeffrey M. Lee's(adsbygoogle = window.adsbygoogle || []).push({}); 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).

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Natural graded derivation.

**Physics Forums | Science Articles, Homework Help, Discussion**