A Invariance of Commutator Relations

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fresh_42

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Does anybody know of examples, in which groups defined by ##[\varphi(X),\varphi(Y)]=[X,Y]## are investigated? The ##X,Y## are vectors of a Lie algebra, so imagine them to be differential operators, or vector fields, or as physicists tend to say: generators. The ##\varphi## are thus linear transformations of named Lie algebra that preserve the commutation relations.
 

martinbn

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So, you are asking about groups of automorphisms of Lie algebras?
 

fresh_42

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So, you are asking about groups of automorphisms of Lie algebras?
No. That would be ##[\varphi(X),\varphi(Y)]=\varphi([X,Y])##. I asked about ##\ldots = [X,Y]\,.##

In other words: a homomorphism is of the form ##\varphi^* \otimes \varphi^* \otimes \varphi^{-1}=\operatorname{id}## and I am interested in ##\varphi^* \otimes \varphi^* \otimes 1=\operatorname{id}\,.##
 
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