Timeline for Maximality of the maximal tensor product of C*-algebras
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2016 at 15:33 | comment | added | Ruy | Dear @Sabrina, in case of unital C*-algebras you need to add a relation expressing that the unit of $A$ coincides with the unit of $B$. Thus $C^*(A,B\,|\,[A,B]=0,\ 1_A=1_B)\simeq A⊗_{max}B$. In fact I just edited my question to account for a similar problem with units in the paragraph about free product. Except for this small glitch, what you say is exactly what I have in mind. The weaker condition I want is precisely that $A$ and $B$ commute as sets, not necessarily commuting elementwise. Part of the trouble is that you cannot express this condition in terms of relations. | |
| Nov 16, 2016 at 15:24 | history | edited | Ruy | CC BY-SA 3.0 |
added 80 characters in body
|
| Nov 16, 2016 at 2:28 | comment | added | Sabrina Gemsa | You have $C^*(A,B| [A,B]=0)\cong A\otimes_{max}B$ for $A$ and $B$ unital, where $C^*(A,B| [A,B]=0)$ is the universal c*algebra generated by commuting copies of A and B. And you want something weaker, right? | |
| Nov 15, 2016 at 23:31 | history | asked | Ruy | CC BY-SA 3.0 |