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Rigidity of pseudofunction algebras of ample groupoids (2506.09563v1)

Published 11 Jun 2025 in math.OA, math.DS, and math.GR

Abstract: We show that a Hausdorff, ample groupoid $\mathcal{G}$ can be completely recovered from the $I$-norm completion of $C_c(\mathcal{G})$. More generally, we show that this is also the case for the algebra of symmetrized $p$-pseudofunctions, as well as for the reduced groupoid $Lp$-operator algebra, for $p\neq 2$. Our proofs are based on a new construction of an inverse semigroup built from Moore-Penrose invertible partial isometries in an $Lp$-operator algebra. Along the way, we verify a conjecture of Rako\v{c}evi\'{c} concerning the continuity of the Moore-Penrose inverse for $Lp$-operator algebras.

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