# Are there any infinite dimensional subalgebras of the Witt algebra?

The Lie bracket of elements of the Witt algebra is given by:

$[L_m,L_n]=(m-n)L_{m+n}$

Are there any infinite dimensional subalgebras of the Witt algebra that are not isomorphic to the Witt algebra itself?

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the positive part? or some subalgebra like this. –  user81130 Jun 5 '13 at 20:26