Timeline for Formally real Jordan algebras
Current License: CC BY-SA 2.5
5 events
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| Nov 11, 2010 at 14:13 | comment | added | Harald Hanche-Olsen | John, I was painfully aware at the time that I did not really answer your question. Still, I hoped (and still hope) that at least it did shed some light on some corner of it. Regarding ideals, I am sure you are aware that in a unital C*-algebra (or unital Banach algebra more generally), the closure of a nontrivial ideal is again nontrivial, since a neighbourhood of the unit consists of invertible elements. Non-unital algebras is presumably a whole different kettle of fish. | |
| Nov 11, 2010 at 5:58 | comment | added | John Baez | Thanks, Harald. No thanks, Allen. :-) I would really like to see a wild multitude of simple formally real Jordan algebras. I'm not sure I see them yet. Harald, I guess you're hinting that I can get such a thing from any C*-algebra that lacks nontrivial star-ideals. But this reminds me that my question said nothing about a norm, or topology. I know lots of infinite-dimensional C*-algebras that lack nontrivial closed star-ideals, but how about C*-algebras that don't have any nontrivial star-ideals? | |
| Nov 9, 2010 at 15:09 | comment | added | Harald Hanche-Olsen | Heh. Well, JB in this context stands for Jordan–Banach. | |
| Nov 9, 2010 at 13:42 | comment | added | Allen Knutson | JB, were you just fishing for someone to mention JB-algebras? | |
| Nov 9, 2010 at 9:54 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |