For Hausdorff, ample groupoids, the I-norm completion of the convolution algebra, the symmetrized p-pseudofunction algebras, and the reduced Lp-operator algebras for p not equal to 2 all determine the groupoid up to isomorphism.
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Rigidity of pseudofunction algebras of ample groupoids
For Hausdorff, ample groupoids, the I-norm completion of the convolution algebra, the symmetrized p-pseudofunction algebras, and the reduced Lp-operator algebras for p not equal to 2 all determine the groupoid up to isomorphism.