simple nuclear $C^*$ algebra [closed]












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Does there exist an infinite dimensional simple nuclear $C^*$ algebra which admits a tracial state?










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closed as off-topic by Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos Jan 18 at 11:27


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    Does there exist an infinite dimensional simple nuclear $C^*$ algebra which admits a tracial state?










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    closed as off-topic by Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos Jan 18 at 11:27


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos

    If this question can be reworded to fit the rules in the help center, please edit the question.



















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      Does there exist an infinite dimensional simple nuclear $C^*$ algebra which admits a tracial state?










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      Does there exist an infinite dimensional simple nuclear $C^*$ algebra which admits a tracial state?







      operator-theory operator-algebras c-star-algebras






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      asked Jan 12 at 6:15









      mathrookiemathrookie

      922512




      922512




      closed as off-topic by Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos Jan 18 at 11:27


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos

      If this question can be reworded to fit the rules in the help center, please edit the question.







      closed as off-topic by Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos Jan 18 at 11:27


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Claude Leibovici, Cesareo, A. Pongrácz, José Carlos Santos

      If this question can be reworded to fit the rules in the help center, please edit the question.






















          1 Answer
          1






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          Yes, many. A prominent example is the CAR-algebra. Another example is the Jiang-Su algebra which is not a UHF-algebra.






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          • $begingroup$
            This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
            $endgroup$
            – user42761
            Jan 12 at 13:03




















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2












          $begingroup$

          Yes, many. A prominent example is the CAR-algebra. Another example is the Jiang-Su algebra which is not a UHF-algebra.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
            $endgroup$
            – user42761
            Jan 12 at 13:03


















          2












          $begingroup$

          Yes, many. A prominent example is the CAR-algebra. Another example is the Jiang-Su algebra which is not a UHF-algebra.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
            $endgroup$
            – user42761
            Jan 12 at 13:03
















          2












          2








          2





          $begingroup$

          Yes, many. A prominent example is the CAR-algebra. Another example is the Jiang-Su algebra which is not a UHF-algebra.






          share|cite|improve this answer









          $endgroup$



          Yes, many. A prominent example is the CAR-algebra. Another example is the Jiang-Su algebra which is not a UHF-algebra.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 12 at 8:47







          user42761



















          • $begingroup$
            This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
            $endgroup$
            – user42761
            Jan 12 at 13:03




















          • $begingroup$
            This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
            $endgroup$
            – user42761
            Jan 12 at 13:03


















          $begingroup$
          This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
          $endgroup$
          – user42761
          Jan 12 at 13:03






          $begingroup$
          This is also no obstruction. For example the Jacelon-Razak algebra is an example, see arxiv.org/abs/1006.5397. I am sure there are more basic examples.
          $endgroup$
          – user42761
          Jan 12 at 13:03





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