Timeline for How "nondegenerate" are amalgamated free products of C*-algebras?
Current License: CC BY-SA 3.0
9 events
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| Mar 10, 2016 at 16:00 | answer | added | Chris Ramsey | timeline score: 4 | |
| Mar 8, 2016 at 19:57 | comment | added | Manny Reyes | @ChrisRamsey Your continued historical notes are most appreciated! Somehow I hadn't noticed Paschke's claim, but I agree with you that this does not seem to follow from Blackadar's proof (or at least not immediately). At this point I'm even curious to hear if anyone has suspicions about whether non-degeneracy should hold, both in case $C = \mathbb{C}$ and in general. | |
| Mar 8, 2016 at 18:26 | comment | added | Chris Ramsey | The mystery deepens: Paschke in his review of Avitzour's paper (ams.org/mathscinet-getitem?mr=654842) declares that Blackadar's Theorem 3.1 proves non-degeneracy. However, I do not believe this statement. | |
| Feb 23, 2016 at 21:36 | comment | added | Manny Reyes | @ChrisRamsey Thank you for that observation! Tracing back the references in Cuntz's paper, I see that the following, earlier paper of L.G. Brown refers to $\| \cdot \|$ a seminorm (but doesn't seem to discuss the question of whether it is truly a norm): theta.ro/jot/archive/1981-006-001/1981-006-001-012.pdf | |
| Feb 20, 2016 at 14:36 | comment | added | Chris Ramsey | In "The K-groups of free products of C$^*$-algebras" Cuntz says you must divide the algebraic free product by the null space of $\|\cdot\|$ but does not provide an example of when this is non-trivial. So either he knew of a degenerate example or your question was unknown in 1982. | |
| Feb 4, 2016 at 21:08 | comment | added | Manny Reyes | @YCor Thank you. I was aware of this type of construction in the literature. My (admittedly vague) understanding is that the non-degeneracy results for such graph C*-algebras again tend to show that vertex and edge groups embed, but probably don't give full information about the relationship with objects universally constructed in the category of rings. But I would be very happy if someone could tell me otherwise! | |
| Feb 3, 2016 at 22:37 | comment | added | YCor | Possibly relevant: arxiv.org/abs/1307.5609 | |
| Feb 3, 2016 at 21:18 | history | edited | Manny Reyes |
Added relevant tag
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| Feb 1, 2016 at 14:34 | history | asked | Manny Reyes | CC BY-SA 3.0 |