Actions of finite groups on finite von Neumann algebras and the relative entropy

Satoshi KAWAKAMI; Hiroaki YOSHIDA

doi:10.2969/jmsj/03940609

Satoshi KAWAKAMI, Hiroaki YOSHIDA

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ジャーナルフリー

1987 年 39 巻 4 号 p. 609-626

DOI https://doi.org/10.2969/jmsj/03940609

詳細

Published: 1987 Received: 1985/07/17 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Osamu Takenouchi on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) O. Besson, Sur l'entropie des automorphismes des algèbres de von Neumann finies, Thesis, 1985.
2) A. Connes, Une classification des facteurs de type III, Ann. Sci. École Norm. Sup., 4me série, t. 6, fasc. 2 (1973), 133-152.
3) A. Connes, Periodic automorphisms of the hyperfinite factor of type II₁, Acta Sci. Math., 39 (1977), 39-66.
4) A. Connes and E. Stormer, Entropy for automorphisms of II₁ von Neumann algebras, Acta Math., 134 (1975), 288-306.
5) J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1969.
6) V. F. R. Jones, Actions of finite groups on the hyperfinite type II₁ factor, Mem. Amer. Math. Soc., 237 (1980).
7) V. F. R. Jones, Index for subfactors, Invent. Math., 72 (1983), 1-25.
8) Y. Katayama, A duality for an outer action of a countable abelian group on a hyperfinite factor of type II₁, preprint.
9) S. Kawakami and H. Yoshida, A decomposition of Jones' index associated with the Galois group, preprint.
10) S. Kawakami and H. Yoshida, Reduction theory on the relative entropy, preprint.
11) M. Nakamura and Z. Takeda, On the fundamental theorems of the Galois theory of finite factors, Proc. Japan Acad., 36 (1960), 313-318.
12) M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup., 19 (1986), 57-106.
13) M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310.
14) H. Umegaki, Conditional expectations in operator algebra I, Tohoku Math. J., 6 (1954), 358-362.
15) H. Yoshida, On crossed products and the relative entropy, Math. Japon., 30 (1985), 981-988.

Right : [1] O. Besson, Sur l'entropie des automorphismes des algèbres de von Neumann finies, Thesis, 1985.
[2] A. Connes, Une classification des facteurs de type III, Ann. Sci. École Norm. Sup., 4me série, t. 6, fasc. 2 (1973), 133-152.
[3] A. Connes, Periodic automorphisms of the hyperfinite factor of type II₁, Acta Sci. Math., 39 (1977), 39-66.
[4] A. Connes and E. Stormer, Entropy for automorphisms of II₁ von Neumann algebras, Acta Math., 134 (1975), 288-306.
[5] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1969.
[6] V. F. R. Jones, Actions of finite groups on the hyperfinite type II₁ factor, Mem. Amer. Math. Soc., 237 (1980).
[7] V. F. R. Jones, Index for subfactors, Invent. Math., 72 (1983), 1-25.
[8] Y. Katayama, A duality for an outer action of a countable abelian group on a hyperfinite factor of type II₁, preprint.
[9] S. Kawakami and H. Yoshida, A decomposition of Jones' index associated with the Galois group, preprint.
[10] S. Kawakami and H. Yoshida, Reduction theory on the relative entropy, preprint.
[11] M. Nakamura and Z. Takeda, On the fundamental theorems of the Galois theory of finite factors, Proc. Japan Acad., 36 (1960), 313-318.
[12] M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup., 19 (1986), 57-106.
[13] M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310.
[14] H. Umegaki, Conditional expectations in operator algebra I, Tôhoku Math. J., 6 (1954), 358-362.
[15] H. Yoshida, On crossed products and the relative entropy, Math. Japon., 30 (1985), 981-988.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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