Sources, authorship and component terms

The seventeen lessons and solutions were written by GPT-6.1 Sol (OpenAI). Self-checked by the writing AI. Included supporting readings state their own authorship. The original course text uses CC0 1.0. The independently written elliptic-analysis readings and original course figures also carry CC0 1.0, with their exact sources, credits and component records retained. The supporting reading records identify the terms of each component.

S. Sundar’s continuous-isometry construction is adapted in Lesson 10, Theorem 10C.1, under CC0 1.0. The adaptation completes the dilation and endpoint arguments, corrects the signs and range intersections, and relates the construction to Green imprimitivity. The supplied original TeX fragment and component notice accompany the proof.

The worked checkpoint A state’s seminorm remembers one column in the GNS reading is adapted from Abraham Anton Westerbaan, The Category of Von Neumann Algebras (2019), supplied LaTeX. The exercise and its added worked solution retain CC BY 4.0. The component notice identifies the exact source version and the adaptation. The remaining original GNS text and its continuity diagram use CC0 1.0.

MathJax uses Apache 2.0; font notices accompany its runtime. External works below retain their own terms.

References

• Bruce Blackadar, Operator Algebras: Theory of C*-Algebras and von Neumann Algebras, Author revision, 8 February 2017.
• Bruce Blackadar, K-Theory for Operator Algebras, Second edition, corrected author copy.
• Dana P. Williams, Crossed Products of C*-Algebras, Author draft version 3.1, 6 September 2006.
• Siegfried Echterhoff, Crossed products, the Mackey–Rieffel–Green machine and applications, arXiv:1006.4975v2, 24 August 2011.
• Ruy Exel, Partial Dynamical Systems, Fell Bundles and Applications, arXiv:1511.04565v2, 29 August 2017.
• Guillermo Cortiñas (editor); Jonathan Rosenberg and Ralf Meyer (contributions used), Topics in Noncommutative Geometry, Clay Mathematics Proceedings 16, 2012.
• Alain Connes, Noncommutative Geometry, 1994 author electronic edition.
• Yuezhao Li, Groupoid C*-algebras, 7 February 2024 revision.
• Paul S. Muhly and Dana P. Williams, Renault’s Equivalence Theorem for Groupoid Crossed Products, New York Journal of Mathematics Monographs 3, 2008.
• Aidan Sims and Dana P. Williams, Renault’s equivalence theorem for reduced groupoid C*-algebras, arXiv:1002.3093v1, 16 February 2010.
• Dominik Gruber, Groups with graphical C(6) and C(7) small cancellation presentations, arXiv:1210.0178v2, 24 July 2014.
• Alain Connes and Georges Skandalis, The Longitudinal Index Theorem for Foliations, Publ. RIMS 20 (1984), 1139–1183.
• Michel Hilsum and Georges Skandalis, Morphismes K-orientés d’espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. ENS 20 (1987), 325–390.
• Daniel A. Spielman, Spectral and Algebraic Graph Theory, Draft, 2 April 2025.
• Louis Esperet and Ugo Giocanti, Optimization in graphical small cancellation theory, arXiv:2306.03474v2, 16 June 2023.
• Maria Paula Gomez Aparicio, Pierre Julg and Alain Valette, The Baum–Connes conjecture: an extended survey, arXiv:1905.10081v1, 24 May 2019.
• Hermann Schulz-Baldes and Tom Stoiber, Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems, arXiv:2206.07781v2, 9 November 2022.
• Dana P. Williams, Haar systems on equivalent groupoids, arXiv:1501.04077v1, 16 January 2015; 2016 publication.
• Aidan Sims, Hausdorff étale groupoids and their C*-algebras, arXiv:1710.10897v2, 4 October 2018.
• Aidan Sims and Dana P. Williams, Amenability for Fell bundles over groupoids, arXiv:1201.0792v1, 4 January 2012.
• Jean-Louis Tu, The Baum–Connes conjecture for groupoids, 1999 survey.
• Claire Anantharaman-Delaroche, Amenability, exactness and weak containment property for groupoids, arXiv:2306.17613v2, 9 August 2023.
• Rufus Willett, A non-amenable groupoid whose maximal and reduced C*-algebras are the same, Münster Journal of Mathematics 8 (2015).
• Yuri A. Kordyukov, Noncommutative geometry of foliations, arXiv:math/0504095v2, 6 May 2006.
• Marta Macho-Stadler, Foliations, groupoids, and the Baum–Connes conjecture, 2003 author article.
• Siegfried Echterhoff, Crossed products and the Mackey–Rieffel–Green machine, arXiv:1006.4975v4, 13 June 2017.
• N. P. Landsman, Lecture Notes on C*-Algebras, Hilbert C*-modules, and Quantum Mechanics, Draft 8 April 1998; arXiv:math-ph/9807030v1, 24 July 1998.
• S. Sundar, Notes on C*-algebras, arXiv:2505.17456v1, 23 May 2025.
• Alcides Buss, Ralf Meyer and Chenchang Zhu, A higher category approach to twisted actions on C*-algebras, arXiv:0908.0455v1, 4 August 2009; published 2013.
• Kevin Aguyar Brix, Toke Meier Carlsen and Aidan Sims, Some results regarding the ideal structure of C*-algebras of étale groupoids, arXiv:2211.06126v2, 3 January 2024.
• Scott M. LaLonde, On some permanence properties of exact groupoids, arXiv:1703.05190v3, 6 November 2018; published 2020.

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