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January 31st, 2014, 10:02 AM  #1  
Newbie Joined: Oct 2012 Posts: 5 Thanks: 0  Factor space of Lie Algebras
In Roger Carter's Lie Algebras of Finite and Affine Type, Proposition 1.7(iii) states that for a Lie algebra , Quote:
 
February 1st, 2014, 04:31 AM  #2 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88  Re: Factor space of Lie Algebras
Isn't I an ideal of L? There seems to be to be no guarantee than I is contained within H. Half the battle in such a statement seems to be to be in showing I is an ideal of the subalgebra I + H (if I recall correctly, ideals are subalgebras, but not vice versa, necessarily), and that I?H is an ideal of H. The isomorphism in question is probably intended to be, for x in I, y in H: (x + y) + I > y + (I?H) 
February 2nd, 2014, 01:45 AM  #3 
Newbie Joined: Oct 2012 Posts: 5 Thanks: 0  Re: Factor space of Lie Algebras
Oh, of course, H/I does not make sense unless I is a subset of H. That is the reason why we have to add I to H first. Thanks for your answer! 

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algebras, factor, lie, space 
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