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
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .