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Amenability of Discrete Semigroup Flows

  • Author / Creator
    Loliencar, Prachi
  • A discrete flow (S,X) is a semigroup S acting on a set X where both S, and X are equipped with the discrete topology. Amenability of semigroups is a topic that explores the existence of measures that are invariant under the semigroup multiplication. The goal of this thesis is to generalize these results to a semigroup acting on a set, i.e. a flow, so that the invariance is with respect to the action. We start out in Chapter 1 by giving some preliminaries that are important for the results in this thesis. Chapter 2 generalizes basic theorems characterizing amenability and gives sufficient and necessary conditions for the same. We discuss some relevant topics such as the Hahn-Banach extension theorem and an application of flow amenability - a fixed point theorem. Next, in Chapter 3, we discuss various Folner conditions - combinatorial properties that characterize aspects of amenability. Finally, in Chapter 4, we discuss the flow stucture of the Stone-Cech compactification of a flow. We then discuss the concept of density of means and apply some properties of Folner nets. In Chapter 5 we briefly get into reversible invariance - a property that is equivalent to amenability in groups (and group flows).

  • Subjects / Keywords
  • Graduation date
    2015-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R37W67D8D
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Li, Michael Y. (Mathematical and Statistical Sciences)
    • Troitsky, Vladimir G. (Mathematical and Statistical Sciences)
    • Lewis, James D. (Mathematical and Statistical Sciences)
    • Runde, Volker (Mathematical and Statistical Sciences)