Vector Product in C³: Explained & Standard Basis

[koolmodee]

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

 

[D H]

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.

 

[koolmodee]

Thanks D H!