I know I should be able to look this up but am having trouble this morning.(adsbygoogle = window.adsbygoogle || []).push({});

I would like to know the Lie Algebra structure of the three sphere. In particular I'd like to express it in terms of the left invariant vector fields that are either tangent to the fibers of the Hopf fibration or perpendicular to it. By this I mean express the algebra in terms if an ortho-normal left invariant basis one of whose elements is tangent to the fiber circles of the Hopf fibration.

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# Lie Algebra of S3

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