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Regarding terminologies, I want to confirm if the generators of the Lie group are elements of the Lie algebra. In that case, exponentiating the matrix representation of the basis of the Lie algebra (which should be the Lie group generators) should give us the the elements of the continuous Lie group, right?
What about the Lie algebra generators? Are they having any role in generating the Lie group?

Anandjm
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    Have you seen https://physics.stackexchange.com/q/65141? – Nihar Karve Dec 28 '20 at 08:53
  • Yeah I did, but I wanted to make sure if I what I have understood was correct. – Anandjm Dec 28 '20 at 12:34
  • Exponentiation of the Lie algebra can only give the connected component of the identity in the best case. This question is furthermore not completely trivial. "Lie Algebra generators" probably reders to a basis pf the Lie algebra. In that case you can get any Lie algebra element as a linear combination. – Adomas Baliuka Dec 28 '20 at 14:49

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