Partial actions on quotient spaces and globalization

• Martínez, Luis ^[1] ; Pinedo, Héctor ^[2] ; Villamizar, Andrés ^[3]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
  3. [3] Universidad de Pamplona

     Universidad de Pamplona

     Colombia

     

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 125-141
• Idioma: inglés
• DOI: 10.4995/agt.2024.17810
• Enlaces
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• Resumen

  • Given a partial action of a topological group G on a space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable, and having invariantmetric. Further, for a normal subgroup H, we introduce and study a partial action of G/H on the orbit space of X; applications to invariant metrics and inverse limits are presented.

• Referencias bibliográficas
  • F. Abadie, Enveloping actions and Takai duality for partial actions. Journal of Funct. Anal. 197 (2003), 14-67. https://doi.org/10.1016/S0022-1236(02)00032-0
  • S. A. Antonyan, Equivariant embeddings into G-AR's, Glasnik Matematički 22 (42) (1987), 503-533.
  • A. Baraviera, R. Exel, D. Gonçalves, F. B. Rodrigues and D. Royer, Entropy for partial actions of Z, Proc. Amer. Math. Soc. 150 (2022), 1089-1103....
  • S. De Neymet and R. Jiménez, Introducción a los grupos topológicos de transformaciones, Aportaciones matemáticas: Textos, 2005.
  • M. Dokuchaev, Recent developments around partial actions, Sao Paulo J. Math. Sci. 13, no. 1 (2019), 195-247. https://doi.org/10.1007/s40863-018-0087-y
  • M. Dokuchaev and R. Exel, The ideal structure of algebraic partial crossed products, Proc. Lond. Math. Soc. (3) 115 (2017), no. 1, 91-134....
  • J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
  • R. Exel, Circle actions on $C^*$-algebras, partial automorphisms and generalized Pimsner-Voiculescu exact sequences, J. Funct. Anal. 122,...
  • R. Exel, Partial dynamical systems, Fell bundles and applications, Mathematical surveys and monographs; volume 224, Providence, Rhode Island:...
  • R. Exel, T. Giordano and D. Gonçalves, Enveloping algebras of partial actions as groupoid $C^*$-algebras, J. Operator Theory 65 (2011), 197-210.
  • D. Gonçalves, J. Öinert and D. Royer, Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics,...
  • 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 E. Ramírez, Partial actions of groups on hyperspaces, Appl. Gen. Topol. 23, no. 2 (2022), 255-268. https://doi.org/10.4995/agt.2022.15745
  • L. Martínez, H. Pinedo and A. Villamizar, Partial actions of groups on profinite spaces, Appl. Gen. Topol., to appear.
  • 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
  • J. C. Quigg and I. Raeburn, Characterizations of crossed products by partial actions, J. Operator Theory 37 (1997), 311-340.
  • M. Tkačenko, L. Villegas, C. Hernández and O. Rendón, Grupos topológicos, SEP, 1997.