# Contents

## Definition

(AD-Renault 00) Recalled for instance in (Sims-Williams 12, p. 4).

## Properties

### Groupoid convolution algebra

###### Proposition

The groupoid convolution algebra of an amenable topological groupoid is in the bootstrap category.

(Tu 99, prop. 10.7), recalled as (Uuye 11, example 3.6).

###### Proposition

For an amenable Lie groupoid $\mathcal{G}$, the full groupoid convolution algebra and the reduced one are naturally isomorphic.

This is due to (AD-Renault 00), recalled for instance as (ANS 05, prop. 1.9)

## References

• Aidan Sims, Dana P. Williams, Amenability for Fell bundles over groupoids (arXiv:1201.0792)
• Johannes Aastrup, Ryszard Nest, Elmar Schrohe, A Continuous Field of C-algebras and the Tangent Groupoid for Manifolds with Boundary_ (arXiv:math/0507317)
• Jean-Louis Tu, La conjecture de Baum-Connes pour les feuilletages moyennables, K-Theory 17 (1999), no. 3, 215–264. MR 1703305 (2000g:19004) (Portico, subscription needed)

Revised on August 15, 2013 02:05:35 by David Roberts (211.27.208.168)