Timeline for The coproduct on the cohomology of a Hopf algebra
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 11 at 10:08 | comment | added | QGravity | @TheoJohnson-Freyd Is this Hopf algebra cohomology $Ext_𝐻(𝑘,𝑘)$ the analog of group cohomology? By this I mean, whether for a group algebra $H=kG$ $H^n(kG,A)$ ($Ext_H(k,k)$) is isomorphic to $H^n(G,A^\times)$, where $A$ is a commutative algebra and $A^\times$ is its multiplicative group of invertible elements. | |
| Feb 13, 2012 at 0:13 | answer | added | Ralph | timeline score: 11 | |
| Feb 8, 2012 at 15:01 | comment | added | James Griffin | My intuition is that Theo is right. Does the construction you have in mind work for any coproduct, or does it have to be cocommutative? | |
| Feb 7, 2012 at 20:32 | comment | added | Mariano Suárez-Álvarez | Theo, the coproduct is constructed much as one constructs the Pontryagin multiplication on the singular homology of a Lie group. (The Yoneda algebra is a commutative algebra under the Yoneda product, which is better than being am homotopy $E_2$-algebra iirc...) | |
| Feb 7, 2012 at 20:22 | comment | added | Theo Johnson-Freyd | Really? I think the usual thing structure on $\mathrm{Ext}_H(k,k)$ is the structure of homotopy-$E_2$ algebra. In particular, it is a Gerstenhaber algebra, and in characteristic $0$ by formality (hard!) there are no higher "Massey products". But it seems you "use up" the comultiplication on $H$ to define the $E_2$ structure on $\mathrm{Ext}_H(k,k)$. | |
| Feb 7, 2012 at 19:29 | history | asked | Mariano Suárez-Álvarez | CC BY-SA 3.0 |