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Vector product in C³

  1. Dec 6, 2008 #1
    The vector product in C³ is a three dimensional Lie algebra. Taking the standard basis (e_1,e_2,e_3) of C³, the brackets can be defined by the relations:

    [e_1,e_2]=e_3 [e_1,e_3]=-e_2 [e_2,e_3]=e_1

    That what my book says, but I don't get. But what does the author mean here with the standard basis of C³?

    thank you
  2. jcsd
  3. Dec 6, 2008 #2

    D H

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    Think of it as the same thing as standard basis of R3. Using × rather than the Lie bracket and i, j, k rather than e1, e2, e3, the above translates to i×j=k, i×k=-j, j×k=i.
  4. Dec 6, 2008 #3
    Thanks D H!
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