Timeline for Hochschild (co)homology of A and of Mod_A
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 30, 2010 at 2:39 | comment | added | Kevin Walker | @Mariano: In your second paragraph, did you mean abelian algebras? If not, what about, say, the path algebra of the A_2 quiver? | |
| Jul 30, 2010 at 2:12 | comment | added | Mariano Suárez-Álvarez | @Kevin: an algebra can be seen as a linear category with one object, so let's do that. Next, if $C$ is a linear category, its modules are the functors $C\to\mathrm{Vect}$, and they form a category ${}_C\mathrm{Mod}$. Now, wo linear categories $C$ and $C'$ are Morita equivalent if they have equivalent module categories ${}_C\mathrm{Mod}$ and ${}_{C'}\mathrm{Mod}$. Finally, under any sensible definition, Hochschild cohomology is invariant under Morita equivalences. | |
| Jul 30, 2010 at 2:09 | comment | added | Kevin H. Lin | Despite having tagged this question with "morita-theory", I don't really know anything about Morita theory. In particular, I don't know what it means for an algebra to be Morita equivalent to a category. | |
| Jul 30, 2010 at 2:04 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
added 9 characters in body
|
| Jul 30, 2010 at 1:43 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 2.5 |