{"paper":{"title":"Motzkin Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Georgia Benkart, Tom Halverson","submitted_at":"2011-06-26T22:33:51Z","abstract_excerpt":"We introduce an associative algebra $\\M_k(x)$ whose dimension is the $2k$-th Motzkin number. The algebra $\\M_k(x)$ has a basis of \"Motzkin diagrams,\" which are analogous to Brauer and Temperley-Lieb diagrams, and it contains the Temperley-Lieb algebra $\\TL_k(x)$ as a subalgebra. We prove that for a particular value of $x$, the algebra $\\M_k(x)$ is the centralizer algebra of $\\uqsl$ acting on the $k$-fold tensor power of the sum of the 1-dimensional and 2-dimensional irreducible $\\uqsl$-modules. We show that $\\M_k(x)$ is generated by special diagrams $\\ell_i, t_i, r_i \\ (1 \\le i < k)$ and $p_j "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5277","kind":"arxiv","version":2},"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"}