Approximation entropies in crossed products with an application to free shifts

Nathanial Brown, Marie Choda

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

It is shown that for two dynamical approximation entropies (one C* and one W*) the implementing inner automorphism in a crossed product A ⋊α ℤ has the same entropy value as the automorphism α. Using the techniques in the proof, an example of a highly ergodic non-asymptotically abelian automorphism with topological entropy zero is also given. More specifically, it is shown that the free shifts on the Cuntz algebra script O sign and the reduced free group C*-algebra C* (double-struck F sign) have topological entropy zero.

Original languageEnglish (US)
Pages (from-to)331-346
Number of pages16
JournalPacific Journal of Mathematics
Volume198
Issue number2
DOIs
StatePublished - Jan 1 2001

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Crossed Product
Automorphism
Topological Entropy
Entropy
Approximation
Group C*-algebra
Cuntz Algebra
Zero
Free Group

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Approximation entropies in crossed products with an application to free shifts. / Brown, Nathanial; Choda, Marie.

In: Pacific Journal of Mathematics, Vol. 198, No. 2, 01.01.2001, p. 331-346.

Research output: Contribution to journalArticle

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