On commutativity of diagrams of type ∏1 factors

Jerzy WIERZBICKI

doi:10.2969/jmsj/05010023

Jerzy WIERZBICKI

著者情報

ジャーナルフリー

1998 年 50 巻 1 号 p. 23-42

DOI https://doi.org/10.2969/jmsj/05010023

詳細

Published: 1998 Received: 1994/11/21 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: 論文タイトル訂正内容: Wrong : On commutativity of diagrams of type Π1 factors
Right : On commutativity of diagrams of type ∏1 factors

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 : B) D. Bisch, A note on intermediate subfactors, Pacific J. Math. 163 (1994), 201-216.
GHJ) F. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter Graphs and Towers of Algebras, MSRI Publ. 14, Springer-Verlag, New York, 1989.
J) V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), 1-25.
K) Y. Kawahigashi, Classification of paragroup actions on subfactors, Publ. Res. Inst. Math. Sci. 31 (1995), 481-517.
NT) M. Nakamura and Z. Takeda, On the fundamental theorem of the Galois theory for finite factors, Proc. Japan Acad. 36 (1960), 258-260.
O) A. Ocneanu, Quantum symmetry, differential geometry of finite graphs and classification of subfactors, Tokyo University Seminary Notes 45, 1991.
P1) S. Popa, Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), 253-268.
P2) S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. Math. 50 (1983), 27-48.
P3) S. Popa, Relative dimension, towers of projections and commuting squares of subfactors, Pacific J. Math. 137 (1989), 181-207.
P4) S. Popa, Classification of subfactors: the reduction to commuting square, Invent. Math. 101 (1990), 19-43.
P5) S. Popa,Classification of amenable subfactors of type Π, Acta Math. 172 (1994), 163-255.
P6) S. Popa,Sur la classification des sous-facteurs d'indice fini du facteur hyperfini, C. R. Acad. Sci. Paris 311 (1990), 95-100.
PP1) M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. Ec. Norm. Sup. 19 (1986), 57-106.
PP2) M. Pimsner and S. Popa, Iterating the basic construction, Trans. Am. Math. Soc. 310 (1988), 127-133.
PP3) M. Pimsner and S. Popa, Finite dimensional approximation of pairs of algebras and obstructions for the index, J. Funct. Anal. 98 (1991), 270-291.
S) T. Sano, Commuting co-commuting squares and finite dimensional Kac algebras, Pacific J. Math. 172 (1996), 243-253.
Su) V. S. Sunder, On commuting squares and subfactors, J. Funct. Anal. 101 (1991), 286-311.
Sut) C. Sutherland, Cohomology and extensions of operator algebras H, Publ. Res. Inst. Math. Sci. 16 (1980), 135-174.
ST) I. N. Steward and D. O. Tall, Chapman and Hall, New York, 1987.
SW) T. Sano and Y. Watatani, Angles between two subfactors, J. Operator Theory 32 (1994), 209-241.
SZ) S. Stratila and L. Zsido, Lectures on von Neumann Algebras, Abacus Press/Ed. Academiei, Turnbridge Wells/Bucuresti, 1979.
T) M. Takesaki, Theory of Operator Algebra I, Springer, Berlin, 1979.
Te) T. Teruya, Characteristic intermediate subfactors, Preprint, 1995.
W) Y. Watatani, Index for C*-subalgebras, Memoirs A.M.S. No. 424, 1990.
WW) Y. Watatani and J. Wierzbicki, Commuting squares and relative entropy for two subfactors, J. Funct. Anal. 133 (1995), 329-341.
We) H. Wenzl, Hecke algebras of type A and subfactors, Invent. Math. 92 (1988), 345-383.
Wi) J. Wierzbicki, An estimate of the depth from an intermediate subfactor, Publ. Res. Inst. Math. Sci. 30 (1994), 1139-1144.

Right : [B] D. Bisch, A note on intermediate subfactors, Pacific J. Math. 163 (1994), 201-216.
[GHJ] F. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter Graphs and Towers of Algebras, MSRI Publ. 14, Springer-Verlag, New York, 1989.
[J] V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), 1-25.
[K] Y. Kawahigashi, Classification of paragroup actions on subfactors, Publ. Res. Inst. Math. Sci. 31 (1995), 481-517.
[NT] M. Nakamura and Z. Takeda, On the fundamental theorem of the Galois theory for finite factors, Proc. Japan Acad. 36 (1960), 258-260.
[O] A. Ocneanu, Quantum symmetry, differential geometry of finite graphs and classification of subfactors, Tokyo University Seminary Notes 45, 1991.
[P1] S. Popa, Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), 253-268.
[P2] S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. Math. 50 (1983), 27-48.
[P3] S. Popa, Relative dimension, towers of projections and commuting squares of subfactors, Pacific J. Math. 137 (1989), 181-207.
[P4] S. Popa, Classification of subfactors: the reduction to commuting square, Invent. Math. 101 (1990), 19-43.
[P5] S. Popa,Classification of amenable subfactors of type ∏, Acta Math. 172 (1994), 163-255.
[P6] S. Popa,Sur la classification des sous-facteurs d'indice fini du facteur hyperfini, C. R. Acad. Sci. Paris 311 (1990), 95-100.
[PP1] M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. Ec. Norm. Sup. 19 (1986), 57-106.
[PP2] M. Pimsner and S. Popa, Iterating the basic construction, Trans. Am. Math. Soc. 310 (1988), 127-133.
[PP3] M. Pimsner and S. Popa, Finite dimensional approximation of pairs of algebras and obstructions for the index, J. Funct. Anal. 98 (1991), 270-291.
[S] T. Sano, Commuting co-commuting squares and finite dimensional Kac algebras, Pacific J. Math. 172 (1996), 243-253.
[Su] V. S. Sunder, On commuting squares and subfactors, J. Funct. Anal. 101 (1991), 286-311.
[Sut] C. Sutherland, Cohomology and extensions of operator algebras ∏, Publ. Res. Inst. Math. Sci. 16 (1980), 135-174.
[ST] I. N. Steward and D. O. Tall, Chapman and Hall, New York, 1987.
[SW] T. Sano and Y. Watatani, Angles between two subfactors, J. Operator Theory 32 (1994), 209-241.
[SZ] S. Stratila and L. Zsido, Lectures on von Neumann Algebras, Abacus Press/Ed. Academiei, Turnbridge Wells/Bucuresti, 1979.
[T] M. Takesaki, Theory of Operator Algebra I, Springer, Berlin, 1979.
[Te] T. Teruya, Characteristic intermediate subfactors, Preprint, 1995.
[W] Y. Watatani, Index for C^*-subalgebras, Memoirs A. M. S. No. 424, 1990.
[WW] Y. Watatani and J. Wierzbicki, Commuting squares and relative entropy for two subfactors, J. Funct. Anal. 133 (1995), 329-341.
[We] H. Wenzl, Hecke algebras of type A and subfactors, Invent. Math. 92 (1988), 345-383.
[Wi] J. Wierzbicki, An estimate of the depth from an intermediate subfactor, Publ. Res. Inst. Math. Sci. 30 (1994), 1139-1144.

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

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）