I must apologize if this question sounds dump but if an isomorphism is established between two groups, is it true that their lie algebra is an isomorphism too? My idea is that since the tangent space is sent to tangent space also in the matrix space, both groups' lie algebra will be isomorphism also. For example we have: SU(2) × SU(2) ≈ SO(4) and su(2) × su(2) ≈ so(4).(adsbygoogle = window.adsbygoogle || []).push({});

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# Isomorphism between groups and their Lie Algebra

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