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January 2nd, 2015, 08:43 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 355 Thanks: 1  Lie algebra of Derivations as a functor?
To an associative algebra $A$ one can associate a Lie algebra $\operatorname{Der} A$ of all derivations $D:A\to A$. To any morphism of associative algebras $\alpha:A\to B$, how can one associate a morphism of Lie algebras $\alpha_\ast:\operatorname{Der} A\to \operatorname{Der} B$ or $\alpha^\ast:\operatorname{Der} B\to \operatorname{Der} A$ in a functorial way? 

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algebra, derivations, functor, lie 
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