TY - JOUR
T1 - Tensor-Product Coaction Functors
AU - Kaliszewski, S.
AU - Landstad, Magnus B.
AU - Quigg, J. O.H.N.
N1 - Publisher Copyright:
© 2020 Australian Mathematical Publishing Association Inc.
PY - 2020
Y1 - 2020
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
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U2 - 10.1017/S1446788720000063
DO - 10.1017/S1446788720000063
M3 - Article
AN - SCOPUS:85082426969
SN - 1446-7887
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
ER -