Geodesic
The Minimal Exact Crossed Product
Documenta mathematica, Tome 23 (2018), pp. 2043-2077
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Given a locally compact group G, we study the smallest exact crossed-product functor (A,G,α)↦A⋊E​G on the category of G-C∗-dynamical systems. As an outcome, we show that the smallest exact crossed-product functor is automatically Morita compatible, and hence coincides with the functor ⋊E​ as introduced by P. Baum et al. in their reformulation of the Baum–Connes conjecture [Ann. K-Theory 1, No. 2, 155–208 (2016; Zbl 1331.46064)]. We show that the corresponding group algebra CE∗​(G) always coincides with the reduced group algebra, thus showing that the new formulation of the Baum–Connes conjecture coincides with the classical one in the case of trivial coefficients.
DOI : 10.4171/dm/668
Classification : 46L08, 46L55, 46L80
Mots-clés : exact groups, exotic crossed products, Baum-Connes conjecture, exotic group algebras 
@article{10_4171_dm_668,
     author = {Alcides Buss and Siegfried Echterhoff and Rufus Willett},
     title = {The {Minimal} {Exact} {Crossed} {Product}},
     journal = {Documenta mathematica},
     pages = {2043--2077},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/668},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/668/}
}
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Alcides Buss; Siegfried Echterhoff; Rufus Willett. The Minimal Exact Crossed Product. Documenta mathematica, Tome 23 (2018), pp. 2043-2077. doi: 10.4171/dm/668

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