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Natural graded derivation.

  1. Mar 28, 2012 #1

    MathematicalPhysicist

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    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 Files:

  2. jcsd
  3. Mar 29, 2012 #2

    mathwonk

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    this is a homework type question, i.e. not appropriate.
     
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