Timeline for Two-sided bar construction
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14, 2013 at 17:02 | vote | accept | Dave | ||
| Oct 12, 2013 at 18:19 | comment | added | Dave | If $A$ is just an algebra, then $HH_*(A)$ "measures" how far $A$ is from being a flat $(A\otimes A^{op})$-module, right? | |
| Oct 12, 2013 at 18:18 | comment | added | Dave | Thank you, I wasn't aware of these problems. I was under the impression, that the case when $A$ is a differential, graded algebra would be similar to the case when $A$ is just an algebra. In this case the two-sided bar construction is a free resolution, but apparently the situation is much more complicated in case $A$ is graded, differential...which is a shame, since I now have no idea how to interpret Hochschild homology of a DG-Algebra. What does Hochschild homology of a DG-algebra "measures"? | |
| Oct 12, 2013 at 17:06 | comment | added | Peter May | by a free resolution: in the presence of a differential on A you have to be careful. The modern approach is to ask for cofibrant approximations of DG modules over DGAs in an appropriate model structure. I can refer you to a brand new treatment: front.math.ucdavis.edu/1310.1159 | |
| Oct 12, 2013 at 16:57 | comment | added | Peter May | The problem I think is the meaning of words: what do you mean | |
| Oct 12, 2013 at 14:46 | comment | added | Dave | Thank you very much for this nice explanation. How does $(B=B(A,A,A),d)$ give rise to a free $A\otimes A^{op}$-resolution of $A$? Does one just consider $(B,(-1)^pd^v)$, where $B$ is now only graded by the homological degree? I would like to get to the Hochschild homology $Tor_*^{A\otimes A^{op}}(A,A)$ of $A$ via the resolution arising from the two-sided bar construction. | |
| Oct 12, 2013 at 13:56 | history | answered | Peter May | CC BY-SA 3.0 |