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May 8, 2015 at 2:59 vote accept Sebastien Palcoux
May 7, 2015 at 17:30 comment added Noah Snyder What you should have in mind here as an example of a similar flavor is $\mathbb{C} \subset M_2(\mathbb{C})$ sitting as the scalar matrices. The only intermediate $C^*$ algebra is the diagonal matrices, which has nontrivial center. This example looks exactly the same, except with gradings around that don't actually do anything important.
May 7, 2015 at 15:43 history answered Noah Snyder CC BY-SA 3.0