Sources, authorship and component terms
The lessons give full bibliographies and result-specific credit. The following freely readable sources inform the continuing source comparisons; listing a source does not claim that every page has been read or that every relevant argument has already been integrated.
- Bruce Blackadar, K-Theory for Operator Algebras — 1998, second edition, author's online copy.
- Serge Richard, K-theory for C*-algebras, and beyond — 2015, Spring 2015 lecture notes.
- Allen Hatcher, Vector Bundles and K-Theory — Version 2.2, November 2017.
- John Roe, Lectures on K-Theory and Operator Algebras — 2017, Math 582, Spring 2017 lecture notes.
- Francesca Arici; Bram Mesland, Toeplitz extensions in noncommutative topology and mathematical physics — arXiv:1911.05823v1, 2019-11-13.
- Pierre de la Harpe; Georges Skandalis, Déterminant associé à une trace sur une algèbre de Banach — 1984, published version, Annales de l'Institut Fourier 34(1), 241–260.
- Ruy Exel, Rotation numbers for automorphisms of C* algebras — 1987, published version, Pacific Journal of Mathematics 127(1), 31–89.
- Alain Connes, Noncommutative Geometry — 1994, author's online book.
- Mihai Pimsner; Dan Voiculescu, Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras — 1980, published version, Journal of Operator Theory 4(1), 93–118.
- Marc A. Rieffel, C*-algebras associated with irrational rotations — 1981, published version, Pacific Journal of Mathematics 93(2), 415–429.
- Marc A. Rieffel, Non-Commutative Tori — A Case Study of Non-Commutative Differentiable Manifolds — 1990, Contemporary Mathematics 105, 191–211; author's online preprint.
- Joachim Cuntz, K-theory for certain C*-algebras. II — 1981, published version, Journal of Operator Theory 5(1), 101–108.
- Bruce E. Blackadar, A simple unital projectionless C*-algebra — 1981, published version, Journal of Operator Theory 5(1), 63–71.
- Moritz Weber; Xin Li; Christian Voigt, C*-Algebras and Dynamics: ISem24 Lecture Notes — 2021-02-20.
- Eberhard Kirchberg; Mikael Rørdam, Non-simple purely infinite C*-algebras — 2000; Proposition4.5 compared, absorption inputs not imported.
- Eberhard Kirchberg; Mikael Rørdam, Infinite non-simple C*-algebras: absorbing the Cuntz algebra O-infinity — 2002; Lemma2.2 exact-cutoff mechanism.
- Eberhard Kirchberg, The Classification of Purely Infinite C*-Algebras Using Kasparov’s Theory — 2022 manuscript; Proposition2.2.1 hereditary projection construction.
- Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, Chapter I — Author chapter; §4 Chern axioms4.13, pp.35–36, axiomatic comparison only.
- Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, Chapter II — Author chapter; §1 Prop1.1 and Cor1.2–1.3, pp.1–2; group-completion proof.
- David E. Handelman, Real dimension groups — arXiv:1102.2964v1; Lemmas3–4, pp.2–3, ordered-vector-space comparison.
- Marc A. Rieffel, Projective modules over higher-dimensional non-commutative tori — 1988; exact author copy, pp.297–298 and307–308, orientation and recalled lattice/trace formulas.
- Bruce Blackadar, Classification of C*-Algebras — 4 June2025 preliminary author edition; Choquet-cone definitions and range statements.
Proof references distinguish complete source arguments, theorem statements and historical attribution. The lessons retain their independently written proofs and state any separate prerequisite limits. Continuing literature comparisons do not imply a missing proof.
Authorship and checking
Original exposition, constructions, examples and solutions: GPT-6.1 Sol (OpenAI), Ultra, October 2026. Self-checked by the writing AI. Human review is not claimed. Mathematical results retain the human source credits stated in the lessons.
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Preparation and exact proof-dependency limits · Sources and authorship metadata