Non-commutative lens spaces

Kengo MATSUMOTO; Jun TOMIYAMA

doi:10.2969/jmsj/04410013

Kengo MATSUMOTO, Jun TOMIYAMA

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ジャーナルフリー

1992 年 44 巻 1 号 p. 13-41

DOI https://doi.org/10.2969/jmsj/04410013

詳細

Published: 1992 Received: 1990/07/18 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: 引用文献情報訂正内容: Wrong : B1) B. Blackadar, K-theory for operator algebras. Springer-Verlag, 1986.
BEEK) O. Bratteli, G. Elliott, D. Evans and A. Kishimoto, Non-commutative spheres I, II, preprint.
Bre) B.A. Brenken, Representations and automorphisms of the irrational rotation algebras, Pacific. J. Math., 111 (1984), 257-282.
BDF) L. Brown, R. Douglas and P. Fillmore, Extensions of C^*-algebras and K-homology, Ann. of Math., 105 (1977), 265-324.
Co1) A. Connes, An analogue of the Thom isomorphism for crossed products of a C^*-algebra by an action of R, Advances in Math., 39 (1981), 31-51.
Co2) A. Connes, Non Commutative Differential Geometry. Chapter I: The Chern Character in K-Homology. Chapter II: De Rham Homology and Non Commutative Algebra, Inst. Hautes Etudes Sci. Publ. Math., 62 (1986), 257-360.
CR) A. Connes and M. A. Rieffel, Yang-Mills for non-commutative two-tori, Contemp. Math., Amer. Math. Soc., 62 (1987), 237-266.
E11) G. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra, 38 (1976), 29-44.
E12) G. Elliott, On the K-theory of the C^*-algebra generated by a projective representation of a torsion free discrete abelian group, Operator algebras and group representations, 1, Pitman, 1983, 157-184.
Fug) B. Fuglede, A commutative theory for normal operators, Proc. Nat. Acad. Sci., 36 (1950), 35-40.
He) J. Hempel, 3-Manifolds, Princeton University Press, 1976.
Ja) W. Jaco, Lectures on Three-Manifold Topology, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, Number 43, Amer. Math. Soc. and National Science Foundation, 1980.
Ka) G. Kasparov, The operator K-functor and extensions of C^*-algebras, Akad. Nauk SSSR, Ser. Math., 44 (1980), 571-636; Math. USSR Izvestijia, 16 (1981), 513-572.
Ma1) K. Matsumoto, Non-commutative three dimensional spheres, preprint.
Ma2) K. Matsumoto, Non-commutative three dimensional spheres, II. Non-commutative Hopf fibering, to appear in Yokohama Math. J..
Ma3) K. Matsumoto, Non-commutative 3-spheres, to appear in the Proceedings of Current Topics in Operator Algebras, A Satellite conference of ICM-90, World Scientific Press.
Pe) G.K. Pedersen, C^*-algebras and their automorphism groups, Academic Press, 1979.
PV) M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross products of C^*-algebras, J. Operator Theory, 4 (1980), 93-118.
Put) C.R. Putnam, On normal operators in Hilbert space, Amer. J. Math., 73 (1951), 357-361.
Ri1) M.A. Rieffel, C^*-algebras associated with irrational rotations, Pacifc J. Math. 93 (1981), 415-429.
Ri2) M.A. Rieffel, Deformation quantizations and operator algebras, preprint.
Ro) J. Rosenberg, The role of K-theory in non-commutative algebraic topology, Operator Algebras and K-Theory. Contemporary Mathematics, 10, Amer. Soc., 1982.
RS) J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J., 55 (1987), 431-474.
To1) J. Tomiyama, Invitation to C^*-algebras and topological dynamics, World Scientific Advanced Series in Dynamical Systems, 3, World Scientific Press, 1987.
To2) J. Tomiyama, Topological representation of C*-algebras, Tôhoku Math. J., 14 (1962), 187-204.
Wa) Y. Watatani, Toral automorphisms on irrational rotation algebras, Math. Japonica, 26 (1981), 479-484.
Wo1) S.L. Woronowicz, Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. Res. Inst. Math. Sci., 23 (1987), 117-181.
Wo2) S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys., 111 (1987), 613-665.

Right : [B1] B. Blackadar, K-theory for operator algebras. Springer-Verlag, 1986.
[BEEK] O. Bratteli, G. Elliott, D. Evans and A. Kishimoto, Non-commutative spheres I, II, preprint.
[Bre] B. A. Brenken, Representations and automorphisms of the irrational rotation algebras, Pacific. J. Math., 111 (1984), 257-282.
[BDF] L. Brown, R. Douglas and P. Fillmore, Extensions of C^*-algebras and K-homology, Ann. of Math., 105 (1977), 265-324.
[Co1] A. Connes, An analogue of the Thom isomorphism for crossed products of a C^*-algebra by an action of R, Advances in Math., 39 (1981), 31-51.
[Co2] A. Connes, Non Commutative Differential Geometry. Chapter I: The Chern Character in K-Homology. Chapter II: De Rham Homology and Non Commutative Algebra, Inst. Hautes Etudes Sci. Publ. Math., 62 (1986), 257-360.
[CR] A. Connes and M. A. Rieffel, Yang-Mills for non-commutative two-tori, Contemp. Math., Amer. Math. Soc., 62 (1987), 237-266.
[E11] G. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra, 38 (1976), 29-44.
[E12] G. Elliott, On the K-theory of the C^*-algebra generated by a projective representation of a torsion free discrete abelian group, Operator algebras and group representations, 1, Pitman, 1983, 157-184.
[Fug] B. Fuglede, A commutative theory for normal operators, Proc. Nat. Acad. Sci., 36 (1950), 35-40.
[He] J. Hempel, 3-Manifolds, Princeton University Press, 1976.
[Ja] W. Jaco, Lectures on Three-Manifold Topology, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, Number 43, Amer. Math. Soc. and National Science Foundation, 1980.
[Ka] G. Kasparov, The operator K-functor and extensions of C^*-algebras, Akad. Nauk SSSR, Ser. Math., 44 (1980), 571-636; Math. USSR Izvestijia, 16 (1981), 513-572.
[Ma1] K. Matsumoto, Non-commutative three dimensional spheres, preprint.
[Ma2] K. Matsumoto, Non-commutative three dimensional spheres, II. Non-commutative Hopf fibering, to appear in Yokohama Math. J..
[Ma3] K. Matsumoto, Non-commutative 3-spheres, to appear in the Proceedings of Current Topics in Operator Algebras, A Satellite conference of ICM-90, World Scientific Press.
[Pe] G. K. Pedersen, C^*-algebras and their automorphism groups, Academic Press, 1979.
[PV] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross products of C^*-algebras, J. Operator Theory, 4 (1980), 93-118.
[Put] C. R. Putnam, On normal operators in Hilbert space, Amer. J. Math., 73 (1951), 357-361.
[Ri1] M. A. Rieffel, C^*-algebras associated with irrational rotations, Pacifc J. Math. 93 (1981), 415-429.
[Ri2] M. A. Rieffel, Deformation quantizations and operator algebras, preprint.
[Ro] J. Rosenberg, The role of K-theory in non-commutative algebraic topology, Operator Algebras and K-Theory. Contemporary Mathematics, 10, Amer. Soc., 1982.
[RS] J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J., 55 (1987), 431-474.
[To1] J. Tomiyama, Invitation to C^*-algebras and topological dynamics, World Scientific Advanced Series in Dynamical Systems, 3, World Scientific Press, 1987.
[To2] J. Tomiyama, Topological representation of C^*-algebras, Tôhoku Math. J., 14 (1962), 187-204.
[Wa] Y. Watatani, Toral automorphisms on irrational rotation algebras, Math. Japonica, 26 (1981), 479-484.
[Wo1] S. L. Woronowicz, Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. Res. Inst. Math. Sci., 23 (1987), 117-181.
[Wo2] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys., 111 (1987), 613-665.

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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