Verification of the Equivalence of an Alternate Definition of the Lie Algebra Multiplication of an Lie Group

The definition of the multiplication in the Lie algebra of a Lie group in terms of the Lie bracket of left invariant vector fields is completely standard. It is also possible to define a multiplication in more elementary terms by using second partials of the Lie group product. This report provides a verification of the equivalence of the multiplication obtained under these two definitions.

By: Michael A. O'Connor

Published in: RC20511 in 1996


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