arXiv 1502.062432015-02-22math.DSmath.OA

A Survey of Algebraic Actions of the Discrete Heisenberg Group

Douglas Lind, Klaus Schmidt

备注：: 55 pages with 3 figures
发表信息：: Russian Math. Surveys 70:4 (2015), pp 657-714
DOI：: 10.1070/RM2015v070n04ABEH004957

英文摘要：

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 noncommutative example, where dynamical phenomena related to its noncommutativity 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. We survey here what is known about such actions of the discrete Heisenberg group, providing numerous examples and emphasizing many of the open problems that remain.

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