{
  "abstract": "We describe Hochschild cohomology of Temperley--Lieb algebras by explicit minimal-resolution coordinates and multilinear operations on Kauffman diagrams. For each doubled-line basic algebra, a finite four-term bimodule complex is verified by a signed-shuffle comparison and an augmented contracting homotopy. We compute cocycles and coboundaries and recover the known cup product and Gerstenhaber bracket in explicit representatives. Over $\\mathbb C$, at nonzero root-of-unity loop parameters, we construct a tower-compatible derivation and the marked-circle two-cocycle. Their classes are nonzero on every nonsemisimple block; their cup products therefore represent all positive classes over the centre. Relative full twists give a compact expression for the derivation. Worked planar diagrams distinguish the cup product from insertion and strict cochain equalities from equalities of classes. A finite-lattice section interprets the marked-circle operation as loop-weight response, derives its planar Potts normalization, and exhibits a six-vertex realization. It also shows why passing to a deformable spin representation may annihilate the class with different coefficients. No thermodynamic conclusion is claimed, and the even-strand zero-parameter family remains separate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04022",
  "author_total": 1,
  "authors": [
    {
      "name": "Viktor Lopatkin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3rwfk8dh7m2b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04022",
  "fulltext_url": null,
  "id": "f3rwfk8dh7m2b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04022",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3rwfk8dh7m2b.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04022"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hochschild cohomology of Temperley--Lieb algebras: a Kauffman diagram perspective",
  "title_text": "Hochschild cohomology of Temperley--Lieb algebras: a Kauffman diagram perspective",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/f3rwfk8dh7m2b",
  "venue": "arXiv",
  "versions": []
}