I know it's true but I couldn't find a reference for the following statement:
The exterior algebra of a Lie algebra is a Gerstenhaber algebra.
Could you tell me a book/paper/something where I could read that?
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2Just check that there is a unique way of extending the bracket of the Lie algebra to the whole exterior algebra such that what you get is a Gerstenhaber algebra. It is an easy exercise. – Mariano Suárez-Álvarez Mar 18 '15 at 03:47
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Yes, you are right, thank you. In general, if I have defined a bracket at degree 1 and with that part I'm able to generate the whole algebra I can use the Leibnitz identity to extend the mentioned bracket. – post Mar 18 '15 at 23:04