Non-commutative entropy computations for continuous fields and cross-products

Emmanuel Germain[1]

  • [1] Institut de Mathematique de Jussieu Université Paris 7 Denis Diderot et CNRS 175 rue du Chevaleret 75013 Paris FRANCE

Annales mathématiques Blaise Pascal (2007)

  • Volume: 14, Issue: 1, page 1-16
  • ISSN: 1259-1734

Abstract

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We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C * -algebras and C ( X ) -automorphisms. Each result relies on explicit factorization via matrices.

How to cite

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Germain, Emmanuel. "Non-commutative entropy computations for continuous fields and cross-products." Annales mathématiques Blaise Pascal 14.1 (2007): 1-16. <http://eudml.org/doc/10538>.

@article{Germain2007,
abstract = {We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C$\{\}^*$-algebras and $C(X)$-automorphisms. Each result relies on explicit factorization via matrices.},
affiliation = {Institut de Mathematique de Jussieu Université Paris 7 Denis Diderot et CNRS 175 rue du Chevaleret 75013 Paris FRANCE},
author = {Germain, Emmanuel},
journal = {Annales mathématiques Blaise Pascal},
keywords = {non-commutative dynamical entropy; cross-products; continuous fields},
language = {eng},
month = {1},
number = {1},
pages = {1-16},
publisher = {Annales mathématiques Blaise Pascal},
title = {Non-commutative entropy computations for continuous fields and cross-products},
url = {http://eudml.org/doc/10538},
volume = {14},
year = {2007},
}

TY - JOUR
AU - Germain, Emmanuel
TI - Non-commutative entropy computations for continuous fields and cross-products
JO - Annales mathématiques Blaise Pascal
DA - 2007/1//
PB - Annales mathématiques Blaise Pascal
VL - 14
IS - 1
SP - 1
EP - 16
AB - We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C${}^*$-algebras and $C(X)$-automorphisms. Each result relies on explicit factorization via matrices.
LA - eng
KW - non-commutative dynamical entropy; cross-products; continuous fields
UR - http://eudml.org/doc/10538
ER -

References

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  8. Kenneth J. Dykema, Topological entropy of some automorphisms of reduced amalgamated free product C * -algebras, Ergodic Theory Dynam. Systems 21 (2001), 1683-1693 Zbl1020.46016MR1869065
  9. Uffe Haagerup, Mikael Rordam, Perturbations of the rotation C * -algebras and of the Heisenberg commutation relation, Duke Math. J. 77 (1995), 627-656 Zbl0830.46058MR1324637
  10. Eberhard Kirchberg, N. Christopher Phillips, Embedding of continuous fields of C * -algebras in the Cuntz algebra 𝒪 2 , J. Reine Angew. Math. 525 (2000), 55-94 Zbl0973.46047MR1780427
  11. Eberhard Kirchberg, Simon Wassermann, Exact groups and continuous bundles of C * -algebras, Math. Ann. 315 (1999), 169-203 Zbl0946.46054MR1721796
  12. Narutaka Ozawa, Amenable actions and exactness for discrete groups, C. R. Acad. Sci. Paris Ser. I Math. 330 (2000), 691-695 Zbl0953.43001MR1763912
  13. C. Pop, R. R. Smith, Crossed products and entropy of automorphisms, J. Funct. Anal 206 (2004), 210-232 Zbl1043.46046MR2024352
  14. R. R. Sinclair, The completely bounded approximation property for discrete crossed products, Indiana Univ. Math. J. 46 (1997), 1311-1322 Zbl0907.46051MR1631596
  15. Dan Voiculescu, Dynamical approximation entropies and topological entropy in operator algebras, Comm. Math. Phys. 170 (1995), 249-281 Zbl0824.46079MR1334396

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