I was wondering about the following(adsbygoogle = window.adsbygoogle || []).push({});

Λ=I+iT

T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary.

And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary.

Now I am wondering about introducing the new basis of generators to make the Lie algebra look more like the one from angular momentum

J±=1/2(J_i±i*K_i)

How can this be a generator as it is complex and would make Λ complex therefore in the first expression?

What am I overlooking or misunderstanding here?

Thank you for your help.

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# Generators of Lorentz Lie Algebra being complex?

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