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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Full Groups
verfasst von : Thierry Giordano, David Kerr, N. Christopher Phillips, Andrew Toms
Erschienen in: Crossed Products of C*-Algebras, Topological Dynamics, and Classification
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The notion of full group was introduced in 1959 by H. Dye in his study of orbit equivalence of measured dynamical systems [19] and [20].In the first part of this chapter we will review the definition of full groups in the measurable case. We will then describe some of their properties. In the second part, we will present the different full groups associated to a topological dynamical system (on the Cantor set) and study their properties in comparison with the measurable case. Since their introduction in [39], the so-called topological full groups have been intensively studied and outstanding results obtained. As remarkable surveys on topological full groups and their properties have recently been written (see de Cornulier [14], Juschenko [53], and Matui [66]), we will review only in this section the properties of full groups.