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A quasidiagonal $C^*$-algebra with a nonquasidiagonal maximal tensor square
We construct a separable unital residually finite-dimensional $C^*$-algebra $A$ whose maximal tensor square contains a proper isometry. In particular, $A$ is quasidiagonal whereas $A\tmax A$ is not. The algebra is generated by finite regular representations obtained from congruence quotients of an e
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