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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Lie algebra bundle associated to a Lie group bundle

Refer the paper by Basavavannappa S KIRANAGI(B S KIRANAGI) on Lie Algebra Bundles, Bull. Sci. Math.2 series, 102(1978), 57-62. there are many papers by him.
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