Homoclinic groups, IE groups, and expansive algebraic actions
نویسندگان
چکیده
منابع مشابه
Homoclinic Groups, Ie Groups, and Expansive Algebraic Actions
We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented algebraic action is 1-expansive exactly when it has finite entropy. We also study the local entropy theory for actions of countable amenable groups on compact groups...
متن کاملHomoclinic Group, Ie Group, and Expansive Algebraic Actions
We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented algebraic action is 1-expansive exactly when it has finite entropy. We also study the local entropy theory for actions of countable amenable groups on compact groups...
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This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic Zd-actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains. 2000 Mathematics Subject Classification: 22D...
متن کاملEntropy for expansive algebraic actions of residually finite groups
We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.
متن کاملThe Bernoulli Property for Expansive Z Actions on Compact Groups
We show that an expansive Z2 action on a compact abelian group is measurably isomorphic to a two–dimensional Bernoulli shift if and only if it has completely positive entropy. The proof uses the algebraic structure of such actions described by Kitchens and Schmidt and an algebraic characterisation of the K property due to Lind, Schmidt and the author. As a corollary, we note that an expansive Z...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2014
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-014-0524-1