Timeline for Relating different constructions of the universal compact quantum group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2021 at 13:56 | comment | added | user167952 | Nice argument. Thanks again. | |
| Mar 21, 2021 at 13:38 | comment | added | Stefaan Vaes | Let $\pi : B \to A$ be any surjective $*$-homomorphism between unital C$^*$-algebras and $\omega$ a state on $A$. Put $\varphi = \omega \circ \pi$. Since $\omega(\pi(a)^* \pi(b)) = \varphi(a^* b)$, there is a canonical unitary identification between the GNS-Hilbert spaces of $\omega$ and $\varphi$. This unitary implements the isomorphism between $\pi_\omega(A)$ and $\pi_\varphi(B)$. | |
| Mar 21, 2021 at 13:31 | history | rollback | Stefaan Vaes |
Rollback to Revision 1
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| S Mar 21, 2021 at 13:30 | history | suggested | user167952 | CC BY-SA 4.0 |
Fixed a typo.
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| Mar 21, 2021 at 13:23 | comment | added | user167952 | Maybe one additional question: we want to define $\theta(\pi_B(b)) = \pi_A(\pi(b))$. Why is this well-defined? If $\pi_B(b) = 0$, then $0=h_B(b) = h_A\circ \pi(b)= \langle \pi_A\pi(b)\xi_A, \xi_A\rangle$ but how can we conclude that $\pi_A(\pi(b)) = 0$? | |
| Mar 21, 2021 at 11:07 | review | Suggested edits | |||
| S Mar 21, 2021 at 13:30 | |||||
| Mar 21, 2021 at 10:52 | vote | accept | CommunityBot | ||
| Mar 21, 2021 at 10:52 | comment | added | user167952 | Thank you professor Vaes. This is exactly what I'm looking for. | |
| Mar 21, 2021 at 9:22 | history | answered | Stefaan Vaes | CC BY-SA 4.0 |