REPRESENTATIONS OF CUNTZ ALGEBRAS ON FRACTAL SETS

• MORI Makoto

  Department of Mathematics College of Humanities and Sciences Nihon University

• SUZUKI Osamu

  Department of Mathematics College of Humanities and Sciences Nihon University

• WATATANI Yasuo

  Department of Mathematical Sciences Faculty of Mathematics Kyushu University

抄録

We consider representations of Cuntz algebras on self-similar fractal sets for proper/improper systems of contractions. Natural representations, called Hausdorff representations, are associated with self-similar sets and Hausdorff measures in the case of similitudes in Rⁿ. We completely classify the Hausdorff representations up to unitary equivalence. The complete invariant is the list(λ₁^D, . . . ,λ_N^D), where λ_j is the Lipschitz constant of the j th contraction and D is the Hausdorff dimension of the fractal set. Any non-trivial list can be realized by similitudes on the unit interval. There exists an improper system of contractions such that its representation of a Cuntz algebra on the self-similar fractal set is not unitarily equivalent to any Hausdorff representation for a proper system of similitudes in Rⁿ.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 61 (2), 443-456, 2007

  九州大学大学院数理学研究院

キーワード

• self-similar set
• fractal
• Cuntz algebra
• representation
• <I>C</I>*-algebra

詳細情報

• CRID: 1390282680205477760
• NII論文ID: 110006377556
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.61.443
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/61/2/61_2_443/_pdf
• 本文言語コード: en
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