Analys- och sannolikhetsseminarium

Abstrakt finns enbart på engelska: To every étale groupoid G and 1 ≤ p < ∞, one can associate an Lp-operator algebra called the reduced groupoid Lp-operator algebra, which is the reduced C*-algebra of G when p = 2. If Gand H are isomorphic étale groupoids, then their associated Lp-operator algebras are isomorphic via a diagonal preserving isometric isomorphism. It is an interesting question whether the converse is true. In the case p = 2, there are easy counterexamples, but has been established in the affirmative for second countable étale groupoids such that the interior of the isotropy bundles are abelian and torsion free. When p ≠ 2, however, no counter-example is known, and it has been proved for locally compact groups as well as topologically principal étale groupoids with compact unit space. In this talk, I will show that the question has an affirmative answer for ample groupoids and p ≠ 2.

This is joint work with Eusebio Gardella and Hannes Thiel.