Timeline for Positive maps on finite group algebras and group homomorphisms
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2021 at 17:43 | vote | accept | Edwin Beggs | ||
| Feb 19, 2021 at 1:35 | comment | added | Narutaka OZAWA | @Edwin Beggs: I learned it from Kirchberg's paper (Invent Math 1993) and recorded in my QWEP survey (IJM 2004). A correction on the previous comment: $p$ is in the center of the C*-algebra generated by the range of $f$. In any case, by the Jordan multiplicativity, $f(xy)$ equals to either $f(x)f(y)$ or $f(y)f(x)$ for each $x,y \in G$. The rest is an algebra/combinatorics problem... | |
| Feb 18, 2021 at 22:20 | answer | added | Matthew Daws | timeline score: 2 | |
| Feb 18, 2021 at 21:05 | comment | added | Edwin Beggs | Sorry that is the paper: On Positive Linear Maps Preserving Invertibility - just found that. | |
| Feb 18, 2021 at 19:57 | comment | added | Edwin Beggs | How does the hypothesis imply that we have a Jordan homomorphism? This is very interesting, and this sounds like the critical point! | |
| Feb 18, 2021 at 0:57 | comment | added | Yemon Choi | @NarutakaOZAWA Indeed something about the original question reminded me of M. Walter's theorem concerning isometric isomorphism of Fourier algebras, which would lead to the kind of conclusion that you suggest. | |
| Feb 18, 2021 at 0:51 | comment | added | Narutaka OZAWA | The hypothesis implies that $f\colon {\mathbb C}G\to{\mathbb C}H$ is a Jordan homomorphism. Hence by Stormer's theorem, there is a central projection $p$ in ${\mathbb C}H$ such that $f(\,\cdot\,)p$ is a homomorphism and $f(\,\cdot\,)(1-p)$ is an anti-homomorphism (as suggested in Yemon's answer). Probably, this would lead to that $f$ itself is either a homomorphism or an anti-homomorphism? | |
| Feb 18, 2021 at 0:35 | answer | added | Yemon Choi | timeline score: 6 | |
| Feb 17, 2021 at 23:11 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 5 characters in body
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| Feb 17, 2021 at 22:09 | history | asked | Edwin Beggs | CC BY-SA 4.0 |