Sources and terms

Human mathematical sources support the statements, conventions and arguments developed in these lessons. Their authorship is distinct from the AI-written exposition and checks.

• J. S. Milne, Lie Algebras, Algebraic Groups, and Lie Groups, 2013 author course notes.
• J. S. Milne, Algebraic Groups, Corrected author edition, iAG2022.pdf.
• J. S. Milne, Algebraic Groups, 2017 author PDF.
• Alexander Kirillov Jr., Introduction to Lie Groups and Lie Algebras, 177-page author draft.
• Pavel Etingof, Lie Groups and Lie Algebras I, MIT 18.745, Fall 2020.
• Pavel Etingof, Lie groups and Lie algebras, arXiv:2201.09397v5, 23 May 2026.
• Pavel Etingof, Representations of Lie Groups, MIT 18.757, Fall 2023.
• John C. Baez, The Octonions, Author web treatment; arXiv math/0105155.
• Meinolf Geck, On the construction of semisimple Lie algebras and Chevalley groups, arXiv:1602.04583v5, 26 September 2016.
• Meinolf Geck, Alexander Lang, Canonical structure constants for simple Lie algebras, arXiv:2404.07652v1, 11 April 2024.
• Masaki Kashiwara, Toshiyuki Tanisaki, Parabolic Kazhdan–Lusztig polynomials and Schubert varieties, arXiv:math/9908153v2.
• Stefan Kolb, Quantum symmetric Kac–Moody pairs, arXiv:1207.6036v3, 29 September 2014.
• Kenny De Commer, Sergey Neshveyev, Lars Tuset, Makoto Yamashita, Ribbon braided module categories, quantum symmetric pairs and Knizhnik–Zamolodchikov equations, arXiv:1712.08047v2.
• Wolfgang Soergel, Kazhdan–Lusztig-Polynome und unzerlegbare Bimoduln über Polynomringen, arXiv:math/0403496v2.
• Pierre Deligne, La série exceptionnelle de groupes de Lie, 1996, pp.321–326; IAS freely readable PDF.
• Pierre Deligne, Ronald de Man, La série exceptionnelle de groupes de Lie II, 1996, pp.577–582; IAS freely readable PDF.
• Michael W. Davis, The Geometry and Topology of Coxeter Groups, 2008 first edition; author PDF.
• Friedrich Wagemann, Introduction to Lie algebra cohomology with a view towards BRST cohomology, Notes dated 23 August 2010; exact approved 15-page author PDF.
• Pavel Etingof, 18.755 Lie Groups and Lie Algebras II — Lecture 22: Levi Decomposition, MIT 18.755 Spring2024, Lecture22, printed pp.260–264; exact approved 6-page PDF.
• Juan Camilo Fiallo R., Lie Algebra Cohomology, 2013 university-hosted notes.
• Jim Hefferon, Linear Algebra, Fourth edition, 2020; author textbook.
• Thomas W. Judson, Abstract Algebra: Theory and Applications, 2026 author reader, §16.3.
• Alexander Premet, Helmut Strade, Classification of finite dimensional simple Lie algebras in prime characteristics, arXiv:math/0601380, 2006.
• Holger Brenner, Algebraische Kurven, Osnabrück2025–2026, Lectures3–4.
• The Stacks Project Authors, The Stacks Project, Constructibility and algebraic-geometry background; exact tags cited in lessons.
• Wilhelm Killing, Die Zusammensetzung der stetigen endlichen Transformationsgruppen, Zweiter Theil, Mathematische Annalen33(1889),1–48; archival volume.
• Joseph Bernstein, Israel Gelfand, Sergei Gelfand, Category of g-modules, 1976 original Russian text,10(2),1–8.
• Wolfgang Soergel, Kategorie O, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe, MPI Preprint 1989-46; institutional original PDF.
• Peter Fiebig, The combinatorics of category O over symmetrizable Kac–Moody algebras, arXiv:math/0305378v2, 25 February 2004; exact native HTML.
• Masaki Kashiwara, Representation theory and D-modules on flag varieties, Astérisque173–174(1989),55–109.
• Jean-Luc Brylinski, Masaki Kashiwara, Kazhdan–Lusztig conjecture and holonomic systems, Inventiones Mathematicae64(1981),387–410; author-hosted PDF.
• Maarten Solleveld, Lie algebra cohomology and Macdonald's conjectures, 2002 author-hosted master thesis.
• Ben Elias, Geordie Williamson, The Hodge theory of Soergel bimodules, arXiv:1212.0791v2, 17 February 2014.
• Nicolas Libedinsky, Geordie Williamson, Standard objects in 2-braid groups, arXiv:1205.4206v2.
• Geordie Williamson, Singular Soergel bimodules, arXiv:1010.1283v2, with the v3 normalization erratum inspected.

The individual lessons credit additional human references for their stated context and examples.

Lesson expression and original figures: CC0 1.0. Written and self-checked by GPT-6.1 Sol (OpenAI) in Codex at Ultra. These checks are not human review. The reader uses MathJax under its retained component terms.

Machine-readable source records · Lesson licence · MathJax licence

The independently authored RT-LIE lesson expression and original figures are CC0 1.0. Foundation proofs and opening-lesson integration were contributed by GPT-6 Astra (OpenAI), Codex, Ultra; the retained lesson exposition and checks also credit GPT-6.1 Sol (OpenAI), Codex, Ultra. These AI self-checks are not independent human review.

The offline bundle also includes programme adaptations and selected source components of Jim Hefferon’s work under the recorded CC BY-SA 2.5 terms, and the John M. Erdman finite-Hermitian-spaces component under its recorded CC BY-SA 4.0 terms. Their attribution, source records, licence grants and acknowledgements remain with those components: Linear-algebra component records · Determinant component records. The linked AG-CA fundamental-theorem-of-algebra proof is copied unchanged with its retained source credits; that AG-CA lesson is independently CC0.

For the retained AG-CA page’s historical Ford draft citation, a current freely readable author reference is Timothy J. Ford, Commutative Algebra, author version of 23 September 2026, Chapter 5: Proposition 5.2.2 (Artin–Tate), Proposition 5.2.3 (Zariski’s lemma), Corollary 5.2.4 and Theorems 5.2.7 and 5.2.9 (Nullstellensatz). The exact historical 2008 draft was not located in the bounded check; this current edition has different numbering. The borrowed page and its source credits are retained unchanged.