付録E　参考文献

本文中の [Murphy] などはこの一覧を指す。本文は書名・論文名まで特定して参照し、版に依存するページ番号へは依存しない。

関数解析・作用素環

• [Conway] John B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1990.
• [Murphy] Gerard J. Murphy, C-Algebras and Operator Theory*, Academic Press, 1990.
• [Davidson] Kenneth R. Davidson, C-Algebras by Example*, AMS, 1996.
• [Kadison–Ringrose I] Richard V. Kadison and John R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, AMS, 1997 reprint.
• [Kadison–Ringrose II] Richard V. Kadison and John R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. II, AMS, 1997 reprint.
• [Takesaki I] Masamichi Takesaki, Theory of Operator Algebras I, Springer, 2002.
• [Williams C*] Dana P. Williams, A (Very) Short Course on C-Algebras*, lecture notes, 2024, https://math.dartmouth.edu/~dana/bookspapers/cstar.pdf.
• [Williams Crossed] Dana P. Williams, Crossed Products of C-Algebras*, AMS, 2007, https://doi.org/10.1090/surv/134.
• [Renault] Jean Renault, A Groupoid Approach to C-Algebras*, Springer LNM 793, 1980, https://doi.org/10.1007/BFb0091072.
• [Raeburn–Williams] Iain Raeburn and Dana P. Williams, Morita Equivalence and Continuous-Trace C-Algebras*, AMS, 1998, https://doi.org/10.1090/surv/060.
• [Rieffel 1974] Marc A. Rieffel, “Morita equivalence for C-algebras and W-algebras,” J. Pure Appl. Algebra 5 (1974), 51–96, https://doi.org/10.1016/0022-4049(74)90003-6.
• [Brown–Green–Rieffel] Lawrence G. Brown, Philip Green, and Marc A. Rieffel, “Stable isomorphism and strong Morita equivalence of C-algebras,” Pacific J. Math.* 71 (1977), 349–363, https://doi.org/10.2140/pjm.1977.71.349.

K理論・指数

• [Wegge-Olsen] N. E. Wegge-Olsen, K-Theory and C-Algebras*, Oxford University Press, 1993.
• [Blackadar] Bruce Blackadar, K-Theory for Operator Algebras, 2nd ed., Cambridge University Press, 1998.
• [Williams K] Dana P. Williams, Lecture Notes on K-Theory, https://math.dartmouth.edu/~dana/bookspapers/k-thy.pdf.
• [Atiyah K] Michael Atiyah, K-Theory, Addison–Wesley, 1967.
• [Pimsner–Voiculescu] Mihai Pimsner and Dan Voiculescu, “Exact sequences for K-groups and Ext-groups of certain cross-product C-algebras,” J. Operator Theory* 4 (1980), 93–118, https://eudml.org/doc/217978.
• [Rieffel 1981] Marc A. Rieffel, “C-algebras associated with irrational rotations,” Pacific J. Math.* 93 (1981), 415–429, https://doi.org/10.2140/pjm.1981.93.415.

非可換幾何

• [Connes NCG] Alain Connes, Noncommutative Geometry, Academic Press, 1994, https://alainconnes.org/wp-content/uploads/book94bigpdf.pdf.
• [Connes 1985] Alain Connes, “Noncommutative Differential Geometry,” Publ. Math. IHÉS 62 (1985), 257–360.
• [GBVF] José M. Gracia-Bondía, Joseph C. Várilly, Héctor Figueroa, Elements of Noncommutative Geometry, Birkhäuser, 2001.
• [Várilly] Joseph C. Várilly, “An Introduction to Noncommutative Geometry,” arXiv:physics/9709045, https://arxiv.org/abs/physics/9709045.
• [Connes 1982] Alain Connes, “A survey of foliations and operator algebras,” in Operator Algebras and Applications, Part I, Proc. Symp. Pure Math. 38 (1982), 521–628, https://alainconnes.org/wp-content/uploads/foliations_and_operator_algebras.pdf.
• [Moerdijk–Mrčun] Ieke Moerdijk and Janez Mrčun, Introduction to Foliations and Lie Groupoids, Cambridge University Press, 2003, https://doi.org/10.1017/CBO9780511615450.
• [Muhly–Renault–Williams] Paul S. Muhly, Jean N. Renault, and Dana P. Williams, “Equivalence and isomorphism for groupoid C-algebras,” J. Operator Theory* 17 (1987), 3–22, https://www.jstor.org/stable/24714593.
• [Sims–Williams] Aidan Sims and Dana P. Williams, “Renault’s equivalence theorem for reduced groupoid C-algebras,” J. Operator Theory* 68 (2012), 223–239, https://jot.theta.ro/jot/archive/2012-068-001/2012-068-001-012.pdf.

物理との接続

• [Haag] Rudolf Haag, Local Quantum Physics, 2nd ed., Springer, 1996.
• [Summers] Stephen J. Summers, “Tomita–Takesaki Modular Theory,” arXiv:math-ph/0511034.
• [Yngvason] Jakob Yngvason, “The role of type III factors in quantum field theory,” Reports on Mathematical Physics 55 (2005), 135–147, https://doi.org/10.1016/S0034-4877(05)80009-6.