Add roadmap: Temperley-Lieb diagrams, categories, and algebras#58
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Add roadmap: Temperley-Lieb diagrams, categories, and algebras#58kim-em wants to merge 3 commits into
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Planar matchings, the diagram category and its universal property, the linear category TL(R, d) with its structures, the algebras and Markov trace, cell modules and the semisimplicity classification, Jones-Wenzl projections, and the Karoubi/root-of-unity summits. Suggested.lean elaborates against pinned Mathlib (sorry-stubbed milestones). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…ures Address review: drop the qInt wrapper and bracket notation (quantum integers are (Polynomial.Chebyshev.S R k).eval δ, spoken directly, with [n] as README prose shorthand only); make TLDiagCat and TLCat objects one-field structures around the boundary-point count; correct the rationale for keeping circle counts as data (discarding them silently imposes δ = 1, breaking the universal property). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
qInt R δ n = (Polynomial.Chebyshev.S R (n - 1)).eval δ is the roadmap's one deliberate wrapper, absorbing the [n] = S (n-1) index shift at a single point instead of at every use site. Still no bracket notation. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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This PR adds a roadmap for Temperley-Lieb diagrams, categories, and algebras: planar matchings with their encodings, counting, and dihedral operations; the diagram category (circles as data) with its monoidal and rigid structure and its universal property as a presented monoidal category; the linear category TL(R, δ) with pivotal, spherical, braided, and ribbon instances; the algebras with the e_i presentation theorem, the unnormalized Markov trace, and conditional expectations; cell modules with the Gram determinant formula and the semisimplicity/nondegeneracy classifications; Jones-Wenzl projections with both recursions and the coefficient formula; and the Karoubi envelope with the generic Clebsch-Gordan classification and the root-of-unity quotients, stated as the first fusion categories in a proof assistant. Conventions pin δ = q + q⁻¹, with quantum integers as evaluations of Mathlib's rescaled Chebyshev polynomials, so genericity hypotheses are ring-level statements about δ. Suggested.lean elaborates against pinned Mathlib (sorry-stubbed milestones, allowed in the roadmap library).
The general pivotal/spherical/ribbon API is deliberately not owned here: this roadmap consumes it from the pivotal and spherical categories roadmap (feat: add pivotal and spherical categories roadmap, #57) and repays it with its first diagrammatic instances, so the cross-links in this README resolve once that PR merges. Braid groups, the Kauffman bracket, and the Jones polynomial are declared non-goals for now. Reusable infrastructure kept here: monoidal categories presented by generators and relations, and cellular algebras.
🤖 Prepared with Claude Code