Timeline for Graded $C^*$-algebras can be faithfully represented on a graded Hilbert space
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2012 at 19:37 | vote | accept | m07kl | ||
| May 8, 2011 at 1:57 | answer | added | Dima Shlyakhtenko | timeline score: 3 | |
| May 7, 2011 at 22:17 | comment | added | m07kl | I can prove this for ordinary tensor product,but not for graded tensor product. | |
| May 7, 2011 at 22:16 | comment | added | m07kl | I try to show that the graded representations of $A\widehat{\otimes}B$ on a graded Hilbert space are in natural one-one correspondence with the pairs of graded -homomorphisms $\phi:A \rightarrow C$, $\psi:A\rightarrow C$ with graded commuting ranges, where $C$ is some graded C-algebra. So one direction I need that a graded C∗-algebras can be faithfully represented on a graded Hilbert space. The another direction I need the fact that a graded rep of $A\widehat{\otimes}B$ on a graded Hilbert space $H$ can be restrict to a pair of graded reps on $H$. | |
| May 7, 2011 at 20:16 | comment | added | Rasmus | Hence you can ask more generally, whether every $G$−$C^*$-algebra has a faithful equivariant representation on a $G$-Hilbert space. | |
| May 7, 2011 at 20:13 | comment | added | Rasmus | An equivalent definition of a graded $C^*$−algebra is as a $C^*$−algebra with a $\mathbb Z/2$-action. | |
| May 7, 2011 at 15:49 | comment | added | m07kl | A $\mathbb{Z}/2$ graded C*-algebra is a C*-algebra $A$ with a *-automorphism $\alpha$ st $\alpha^2=1_A$. the even elements is the elements $a$ st $\alpha(a)=a$ and the odd elements is the elements $a$ st $\alpha(a)=-a$. | |
| May 7, 2011 at 14:01 | comment | added | Benjamin Hayes |
What is a graded $C^{*}$-algebra? And what are its odd elements?
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| May 7, 2011 at 11:06 | history | asked | m07kl | CC BY-SA 3.0 |