Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given a Matrix Lie Group, the Lie Bracket is of the associated Lie Algebra is given by the Lie Derivative. Is this always the commutator if we start from a Matrix Lie Group?

Cheers!

share|improve this question
add comment

1 Answer 1

up vote 7 down vote accepted

Yes; one can prove that the Lie bracket in the Lie algebra of the general linear group is the matrix commutator. Any matrix group is a subgroup of this with corresponding subalgebra and the bracket of the subalgebra is just the restriction of the original bracket.

share|improve this answer
    
Cheers, thanks for the quick answer! –  user17574 Aug 5 '13 at 7:59
    
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.