Geodesic
A survey of algebraic actions of the discrete Heisenberg group
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 4, pp. 657-714

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The study of actions of countable groups by automorphisms of compact Abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the simplest non-commutative example, where dynamical phenomena related to its non-commutativity already illustrate many of these connections. The explicit structure of this group means that these phenomena have concrete descriptions, which are not only instances of the general theory but are also testing grounds for further work. This paper surveys what is known about such actions of the discrete Heisenberg group, providing numerous examples and emphasizing many of the open problems that remain. Bibliography: 71 titles.
Keywords: Heisenberg group, expansiveness, entropy.
Mots-clés : algebraic action 
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     author = {D. Lind and K. Schmidt},
     title = {A survey of algebraic actions of the discrete {Heisenberg} group},
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D. Lind; K. Schmidt. A survey of algebraic actions of the discrete Heisenberg group. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 4, pp. 657-714. http://geodesic.mathdoc.fr/item/RM_2015_70_4_a1/