Timeline for Realisation of the noncommutative torus as a universal $ C^{*} $-algebra
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22, 2020 at 2:43 | vote | accept | truebaran | ||
| Feb 8, 2016 at 16:32 | comment | added | Nik Weaver | @truebaran: this seems like a very complete answer to your question, why don't you accept it? | |
| Jan 20, 2016 at 3:31 | comment | added | Transcendental | @Svinepels: Regarding your latest question, there is no set-theoretical issue. If $ \varphi(x) $ is a formula in the first-order language of set theory, and if $ X $ is a set, then according to the Axiom Schema of Specification, $$ \{ x \in X \mid \varphi(x) \} $$ is a set. In Step 8 of my post, $ X = \Bbb{R}_{\geq 0} $, and $ \varphi(x) $ reads “there exist a $ C^{\ast} $-algebra $ A $ and elements $ s,t $ of $ A $ such that $ (A,s,t) $ is a $ C^{\ast} $-representation of $ \mathcal{A}_{\theta} $ and $ x = \| {\pi_{A,s,t}}(a) \|_{A} $”. | |
| Jan 20, 2016 at 2:53 | comment | added | Transcendental | @Svinepels: Hi. I have deleted my answer to your previous question in order to give a more detailed explanation here. A rational non-commutative torus $ A_{\theta} $, where $ \theta \in \Bbb{Q} $, is constructed in exactly the same manner as in my post, but it is not a simple $ C^{*} $-algebra. In fact, we have $ \operatorname{Prim}(A_{\theta}) \cong \Bbb{T}^{2} $ as topological spaces. | |
| Jan 14, 2016 at 16:30 | comment | added | Ulrik | Thanks for the previous answer. Another question: Doesn't it lead to size issues considering the supremum taken over all $C^*$-representations? | |
| Nov 23, 2015 at 17:06 | comment | added | Ulrik | If one were to construct a rational commutative torus, what would one do differently? | |
| Aug 17, 2015 at 4:23 | comment | added | Transcendental | @Branimir: Thanks for the compliment! | |
| Aug 14, 2015 at 22:50 | comment | added | Branimir Ćaćić | +1 I'm very late to the party, but this is an excellent answer. | |
| Feb 22, 2015 at 18:59 | history | answered | Transcendental | CC BY-SA 3.0 |