Timeline for Clifford algebras as deformations of exterior algebras
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2020 at 12:44 | comment | added | Bertram Arnold | Any difference to established conventions is completely due to my own ignorance, and it is definitely bad notation to use the same letters for a complex and its cohomology. I've edited the answer as per your suggestion. | |
| Feb 3, 2020 at 12:44 | history | edited | Bertram Arnold | CC BY-SA 4.0 |
Improved notation for Hochschild complex
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| Feb 3, 2020 at 12:19 | comment | added | Pedro | Is it common for people to write $\mathrm{HH}^*(A)$ for the Hochschild complex of an algebra? Most if not all people I know (except those working with spectra, for example, for which THH would be generally be something you take the homotopy of) would use $C^*(A)$, or some variant thereof, for the complex, and $\mathrm{HH}^*(A)$ for the cohomology of this. Perhaps you're just using a 'topological' notation here for some reason...? | |
| May 10, 2018 at 10:27 | comment | added | Bertram Arnold | Thanks! I tried to be detailed, but here is the short version of the story: Whenever you have a deformation problem, you should first try to understand the corresponding formal deformation problem, which is governed by some dgla. If this dgla is formal, a deformation to all orders is uniquely determined by its first-order deformation, which has to be unobstructed. So a deformation of $\Lambda^*V$ "is" a Poisson structure on $\Pi V^\vee$, of which $\operatorname{Sym}^2(V)$ is a special example. The other answer gives the explicit formula for the multiplication in terms of the Poisson bracket. | |
| May 9, 2018 at 20:03 | vote | accept | fosco | ||
| May 9, 2018 at 20:03 | comment | added | fosco | This is a fascinating answer and it will take me "several years of Sundays" to understand it :-) | |
| May 7, 2018 at 13:08 | history | answered | Bertram Arnold | CC BY-SA 4.0 |