Timeline for Relationship between Hochschild cohomology and Drinfeld centers
Current License: CC BY-SA 3.0
10 events
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| Jan 17, 2015 at 23:02 | vote | accept | Samuel M | ||
| Jan 17, 2015 at 23:02 | comment | added | Samuel M | Will look into that, all of this was very helpful, thanks. | |
| Jan 16, 2015 at 18:51 | comment | added | AAK | @SamuelM, according to Remark 1.5 in the paper, it seems that the Drinfeld centre of $D(A \otimes A^{op})$ will be the $\infty$-category of modules over the Hochschild chain complex of $A \otimes A^{op}$. | |
| Jan 16, 2015 at 1:05 | comment | added | Samuel M | So Hochschild cohomology of the associative algebra $A =$ Ext$^{\bullet}_{A \otimes A^{op}} (A,A)$ is End$_{D(A \otimes A^{op})} (A)$, I wonder what the (Drinfeld) center of $D(A \otimes A^{op})$ is and how it is related to this derived center of $A$? Thank you so much again. | |
| Jan 14, 2015 at 11:24 | history | edited | AAK | CC BY-SA 3.0 |
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| Jan 14, 2015 at 10:26 | comment | added | Samuel M | Thank you again, when I read that Hochschild cohomology of the associative algebra $A$ is a "derived center" I thought it would be equivalent to something like the Drinfeld center of the derived category $D(Mod_{A \otimes A^{op}})$? Or is "derived" referring to something else? Sorry if that doesn't make sense, I might be a bit tired. | |
| Jan 13, 2015 at 15:26 | history | edited | AAK | CC BY-SA 3.0 |
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| Jan 13, 2015 at 0:40 | comment | added | Samuel M | Thank you, this is all still a bit foreign to me, but going by what you wrote and intuition from what I know about Hochschild (co)homology, do you mean that the Drinfeld center of the symmetric monoidal infinity-category of presentable infinity-categories and colimit-preserving functors is the same as the Hochschild cohomology of every associative algebra object in this same category? Does that make sense? | |
| Jan 12, 2015 at 17:42 | history | edited | AAK | CC BY-SA 3.0 |
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| Jan 12, 2015 at 17:36 | history | answered | AAK | CC BY-SA 3.0 |