TY - JOUR

T1 - Tensor-Product Coaction Functors

AU - Kaliszewski, S.

AU - Landstad, Magnus B.

AU - Quigg, J. O.H.N.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Recent work by Baum et al. ['Expanders, exact crossed products, and the Baum-Connes conjecture', Ann. K-Theory 1(2) (2016), 155-208], further developed by Buss et al. ['Exotic crossed products and the Baum-Connes conjecture', J. reine angew. Math. 740 (2018), 111-159], introduced a crossed-product functor that involves tensoring an action with a fixed action, then forming the image inside the crossed product of the maximal-tensor-product action. For discrete groups, we give an analogue for coaction functors. We prove that composing our tensor-product coaction functor with the full crossed product of an action reproduces their tensor-crossed-product functor. We prove that every such tensor-product coaction functor is exact, and if is the action by translation on, we prove that the associated tensor-product coaction functor is minimal, thereby recovering the analogous result by the above authors. Finally, we discuss the connection with the-ization functor we defined earlier, where is a large ideal of.

AB - Recent work by Baum et al. ['Expanders, exact crossed products, and the Baum-Connes conjecture', Ann. K-Theory 1(2) (2016), 155-208], further developed by Buss et al. ['Exotic crossed products and the Baum-Connes conjecture', J. reine angew. Math. 740 (2018), 111-159], introduced a crossed-product functor that involves tensoring an action with a fixed action, then forming the image inside the crossed product of the maximal-tensor-product action. For discrete groups, we give an analogue for coaction functors. We prove that composing our tensor-product coaction functor with the full crossed product of an action reproduces their tensor-crossed-product functor. We prove that every such tensor-product coaction functor is exact, and if is the action by translation on, we prove that the associated tensor-product coaction functor is minimal, thereby recovering the analogous result by the above authors. Finally, we discuss the connection with the-ization functor we defined earlier, where is a large ideal of.

KW - 2010 Mathematics subject classification

KW - 46L55

KW - 46M15

UR - http://www.scopus.com/inward/record.url?scp=85082426969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85082426969&partnerID=8YFLogxK

U2 - 10.1017/S1446788720000063

DO - 10.1017/S1446788720000063

M3 - Article

AN - SCOPUS:85082426969

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

ER -