Timeline for Commutative algebras whose bidual is commutative
Current License: CC BY-SA 3.0
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| Jan 30, 2014 at 15:35 | comment | added | Gro-Tsen | Yes, when I first tried to write a multiplication on the bi-dual (I was trying to work out an explicit example), I failed for the reason you point out. But once you demand that multiplication by $\Phi(a)$ should be the bi-transpose of multiplication by $a$, there's basically only one thing you can write down (maybe linear logicians could prove that it's unique in some deeper sense). And since it's simple enough, associative, and relates to $\Phi$ as one would like, I think I can safely say it's "the correct" formula. (Unless someone can suggest another one! :-) | |
| Jan 29, 2014 at 18:15 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |