{"paper":{"title":"On an algebraic approach to higher dimensional statistical mechanics","license":"","headline":"","cross_cats":["nlin.SI","solv-int"],"primary_cat":"hep-th","authors_text":"Herbert Saleur, P. Martin","submitted_at":"1992-08-24T19:41:51Z","abstract_excerpt":"We study representations of Temperley-Lieb algebras associated with the transfer matrix formulation of statistical mechanics on arbitrary  lattices. We first discuss a new hyperfinite algebra, the Diagram algebra $D_{\\underline{n}}(Q)$, which is a quotient of the Temperley-Lieb algebra appropriate for Potts models in the mean field case, and in which the algebras appropriate for all transverse lattice shapes $G$ appear as subalgebras. We give the complete structure of this subalgebra in the case ${\\hat A}_n$ (Potts model on a cylinder). The study of the Full Temperley Lieb algebra of graph $G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9208061","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}