Dimension groups for subshifts and simplicity of the associated C^*-algebras

抄録

We describe the notion of the dimension group for subshifts in terms of symbolic dynamical system and show that the dimension group is a conjugacy invariant. We will show that the the hereditary subsets invariant under the dimension group au-tomorphism exactly corresponds to the gauge invariant ideals of the associated C<SUP>*</SUP>-algebra \mathcal{O}<SUB>Λ</SUB> for the subshift (Λ, σ). As a result, we give the conditions that the C<SUP>*</SUP>-algebra \mathcal{O}<SUB>Λ</SUB> becomes simple and purely infinite in terms of symbolic dynamics.

収録刊行物

• Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 51(3), 679-698, 1999-07

The Mathematical Society of Japan

各種コード

• NII論文ID(NAID)
10004480705
• NII書誌ID(NCID)
AA0070177X
• 本文言語コード
ENG
• 資料種別
ART
• ISSN
00255645
• NDL 記事登録ID
4818859
• NDL 雑誌分類
ZM31(科学技術--数学)
• NDL 請求記号
Z53-A209
• データ提供元
CJP書誌  CJP引用  NDL  J-STAGE

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