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Quasi-invariant lifts of completely positive maps for groupoid actions
Published online by Cambridge University Press: 19 August 2025
Abstract
Let G be a locally compact, Hausdorff, second countable groupoid and A be a separable, 
$C_0(G^{(0)})$-nuclear, G-
$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant, completely positive and contractive maps from A into a separable, quotient 
$C^*$-algebra. Along the way, we construct the Busby invariant for G-actions.
MSC classification
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
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