Partial actions of groups on hyperspaces
Keywords:Partial action, globalization, hyperspace, monad
Let X be a compact Hausdorff space. In this work we translate partial actions of X to partial actions on some hyperspaces determined by X, this gives an endofunctor 2- in the category of partial actions on compact Hausdorff spaces which generates a monad in this category. Moreover, structural relations between partial actions θ on X and partial determined by 2θ as well as their corresponding globalizations are established.
F. Abadie, Enveloping actions and Takai duality for partial actions, J. Funct. Anal. 197 (2003), 14-67. https://doi.org/10.1016/S0022-1236(02)00032-0
J. Camargo, D. Herrera and S. Macías, Cells and $n$-fold hyperspaces, Colloq. Math. 145, no. 2 (2016), 157-166. https://doi.org/10.1016/j.topol.2015.10.001
K. Choi, Birget-Rhodes expansions of topological groups, Advanced Studies in Contemporary Mathematics 23, no. 1 (2013), 203-211.
M. Dokuchaev, Recent developments around partial actions, S~ao Paulo J. Math. Sci. 13, no. 1 (2019), 195-247. https://doi.org/10.1007/s40863-018-0087-y
M. Dokuchaev and R. Exel, Partial actions and subshifts, J. Funct. Analysis 272 (2017), 5038-5106. https://doi.org/10.1016/j.jfa.2017.02.020
R. Exel, Circle actions on $C^*$-algebras, partial automorphisms and generalized Pimsner-Voiculescu exact sequences, J. Funct. Anal. 122, no. 3 (1994), 361-401. https://doi.org/10.1006/jfan.1994.1073
R. Exel, Partial actions of group and actions of inverse semigroups, Proc. Amer. Math. Soc. 126, no. 12 (1998), 3481-3494. https://doi.org/10.1090/S0002-9939-98-04575-4
R. Exel, Partial dynamical systems, Fell bundles and applications, Mathematical surveys and monographs; volume 224, Providence, Rhode Island: American Mathematical Society, 2017. https://doi.org/10.1090/surv/224
R. Exel, T. Giordano, and D. Gonçalves, Enveloping algebras of partial actions as groupoid $C^*$-algebras, J. Operator Theory 65 (2011), 197-210.
J. Kellendonk and M. V. Lawson, Partial actions of groups, International Journal of Algebra and Computation 14 (2004), 87-114. https://doi.org/10.1142/S0218196704001657
L. Martínez, H. Pinedo and A. Villamizar, Partial actions on profinite spaces, preprint.
S. Nadler and A. Illanes, Hyperspaces: Fundamentals and Recent Advances, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1999.
H. Pinedo and C. Uzcátegui, Polish globalization of Polish group partial actions, Math. Log. Quart. 63, no. 6 (2017), 481-490. https://doi.org/10.1002/malq.201600018
H. Pinedo and C. Uzcátegui, Borel globalization of partial actions of Polish groups, Arch. Mat. Log. 57 (2018), 617-627. https://doi.org/10.1007/s00153-017-0598-8
J. C. Quigg and I. Raeburn, Characterizations of crossed products by partial actions, J. Operator Theory 37 (1997), 311-340.
B. Steinberg, Partial actions of groups on cell complexes, Monatsh. Math. 138, no. 2 (2003), 159-170. https://doi.org/10.1007/s00605-002-0521-0
How to Cite
Copyright (c) 2022 Applied General Topology
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.