Timeline for Bimodules in geometry
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2009 at 19:24 | comment | added | GMRA | Thats true. It was written in haste. I guess I meant that they seem to pop up more often, and perhaps more naturally, when dealing with noncommutative things. But as for the reason for that I do not know. | |
| Oct 26, 2009 at 17:50 | comment | added | Dmitri Pavlov | Grétar, I do not quite follow your reasoning. In the commutative case we can also have A-A-bimodules where the left and right actions are different and so we get a nontrivial A-A-bimodule. | |
| Oct 22, 2009 at 21:48 | comment | added | GMRA | I believe the point Charles is making is the fact that in commutative land giving some abelian group M the structure of a left A-module, is equivalent to giving it the structure of a right A-module. So there is nothing really new happening there. However in noncommutative land giving M an A-A-bimodule structure is harder since you have to find two different module structures that interact nicely. But this is obviously just a partial answer since it only talks about A-A-bimodules and not A-B-bimodules in general. | |
| Oct 22, 2009 at 20:17 | comment | added | Dmitri Pavlov | Well, this is also the case for noncommutative von Neumann algebras: A left M-module is the same thing as a right M^op-module. In particular, an M-N-bimodule is the same thing as a left M⊗N^op-module for an appropriate monoidal structure on von Neumann algebras. This does not imply that we cannot have an interesting theory of bimodules over von Neumann algebras, in fact we do have such a theory. | |
| Oct 22, 2009 at 20:11 | history | answered | Charles Siegel | CC BY-SA 2.5 |