Talk:Equivariant differential form

I think that "invariant element of $$\mathbb{C}[\mathfrak{g}] \otimes \Omega^*(M).$$" shoud be "invariant element of $$\mathbb{C}[\mathfrak{g}^*] \otimes \Omega^*(M).$$"? Basically $$\operatorname{Mor}(\mathfrak{g},\Omega^*(M))=\operatorname{Mor}(\mathfrak{g},\mathbb{C})\otimes\Omega^*(M)=\mathbb{C}[\mathfrak{g}^*]\otimes\Omega^*(M)$$, so I would expect invariant elements to do the same. Of course, the Killing form identifies $$\mathfrak{g}$$ and $$\mathfrak{g}^*$$ but it seems cleaner not to invoke the Killing form.


 * You're correct; "*" is missing (as you can see from your proof as well as one in the article.) -- Taku (talk) 11:14, 7 April 2015 (UTC)


 * Actually it was correct before; I think it's a matter of the notation. In the article (and elsewhere in Wikipedia), we write $$\mathbb{C}[\mathfrak{g}]$$ for the coordinate ring of $$\mathfrak{g}$$ (see ring of polynomial functions). That is, $$\mathbb{C}[\mathfrak{g}] = \operatorname{Sym}(\mathfrak{g}^*)$$. Since "Sym" also appears in literature, that version is now also noted in the article. -- Taku (talk) 11:36, 7 April 2015 (UTC)