{"paper":{"title":"Connected quantized Weyl algebras and quantum cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Christopher D. Fish, David A. Jordan","submitted_at":"2016-11-29T16:50:43Z","abstract_excerpt":"For an algebraically closed field $K$, we investigate a class of noncommutative $K$-algebras called connected quantized Weyl algebras. Such an algebra has a PBW basis for a set of generators $\\{x_1,\\dots,x_n\\}$ such that each pair satisfies a relation of the form $x_ix_j=q_{ij}x_jx_i+r_{ij}$, where $q_{ij}\\in K^*$ and $r_{ij}\\in K$, with, in some sense, sufficiently many pairs for which $r_{ij}\\neq 0$. We classify connected quantized Weyl algebras, showing that there are two types, linear and cyclic, each depending on a single parameter $q$. When $q$ is not a root of unity we determine the pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09721","kind":"arxiv","version":3},"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"}