Abstract
An algebraic ℤd-action is a ℤd-action by automorphisms of a compact abelian group. By Pontryagin duality, there is a one-to-one correspondence between algebraic ℤd-actions and modules over the ring R d of Laurent polynomials with integer coefficients in d commuting variables.
This correspondence establishes a close connection between algebraic and arithmetical properties of R d -modules and dynamical properties of algebraic ℤd-actions, which is the subject of this article.
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Schmidt, K. (2001). The Dynamics of Algebraic ℤd-Actions. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 201. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8268-2_33
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DOI: https://doi.org/10.1007/978-3-0348-8268-2_33
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