caa a22 4500 475738608 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1007/PL00005793 doi (NATIONALLICENCE)springer-10.1007/PL00005793 Isomorphism rigidity of irreducible algebraic ℤd-actions [Elektronische Daten] [Bruce Kitchens, Klaus Schmidt] Abstract. : An irreducible algebraic ℤ d -actionα on a compact abelian group X is a ℤ d -action by automorphisms of X such that every closed, α-invariant subgroup Y⊊X is finite. We prove the following result: if d≥2, then every measurable conjugacy between irreducible and mixing algebraic ℤ d -actions on compact zero-dimensional abelian groups is affine. For irreducible, expansive and mixing algebraic ℤ d -actions on compact connected abelian groups the analogous statement follows essentially from a result by Katok and Spatzier on invariant measures of such actions (cf. [4] and [3]). By combining these two theorems one obtains isomorphism rigidity of all irreducible, expansive and mixing algebraic ℤ d -actions with d≥2. Springer-Verlag Berlin Heidelberg, 2000 Kitchens Bruce Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA (e-mail: brucek@us.ibm.com), USA aut Schmidt Klaus Mathematics Institute, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria, Austria aut Inventiones mathematicae Springer Berlin Heidelberg 142/3(2000-12-01), 559-577 0020-9910 142:3<559 2000 142 222 https://doi.org/10.1007/PL00005793 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00005793 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kitchens Bruce Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA (e-mail: brucek@us.ibm.com), USA aut NATIONALLICENCE 700 1- Schmidt Klaus Mathematics Institute, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria, Austria aut NATIONALLICENCE 773 0- Inventiones mathematicae Springer Berlin Heidelberg 142/3(2000-12-01), 559-577 0020-9910 142:3<559 2000 142 222 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer