How to prove SO(1,3)=SU(2)+SU(2)

fxdung · Oct 24, 2018

The Lie Algebra of SO(1,3) is similar with that of SU(2)+SU(2) or of SO(3)+SO(3). But how do we know SO(1,3) really decomposite to SU(2)+SU(2)?

A. Neumaier · Oct 25, 2018

Your statement is false, hence cannot be proved. Only the conplexified Lie algebras of the groups you write down are isomorphic.

To prove this you exhibit in one of the Lie algebras a basis satisfying the commutation rules of the other. Since complex coefficients appear, complexification is necessary.

How to prove SO(1,3)=SU(2)+SU(2)

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How to prove SO(1,3)=SU(2)+SU(2)

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