Timeline for The support of a module over a equivariant cohomology ring $H^*_G$ is naturally a subset of $\mathfrak g$
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 19, 2016 at 20:59 | comment | added | Matthias Wendt | For the first part, the keyword is Chern-Weil theory. This provides an isomorphism from the ad(G)-polynomials on the Lie algebra to the cohomology of the classifying space. Once $H_G^\ast$ is identified as polynomials on $\mathfrak{g}$ we can naturally view generators of the polynomial ring as coordinates on the Lie algebra. Algebraic geometry then states that the support of a module over a ring $R$ is a closed subset of $Spec(R)$. The spectrum of the polynomial ring is an affine space, which can be identified with the Lie algebra (via the Chern-Weil iso). | |
| Dec 19, 2016 at 19:50 | history | asked | Hang | CC BY-SA 3.0 |