{"paper":{"title":"Representations of $\\bar{U}_q s\\ell(2|1)$ at even roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A M Semikhatov, I Yu Tipunin","submitted_at":"2013-12-18T13:30:08Z","abstract_excerpt":"We construct all projective modules of the restricted quantum group $\\bar{U}_q s\\ell(2|1)$ at an even, $2p$th, root of unity. This $64p^4$-dimensional Hopf algebra is a common double bosonization, $B(X^*)\\otimes B(X)\\otimes H$, of two rank-2 Nichols algebras $B(X)$ with fermionic generator(s), with $H=Z_{2p}\\otimes Z_{2p}$. The category of $\\bar{U}_q s\\ell(2|1)$-modules is equivalent to the category of Yetter--Drinfeld $B(X)$-modules in $C_{\\rho}={}^H_H\\!YD$, where coaction is defined by a universal $R$-matrix $\\rho$. As an application of the projective module construction, we find the associa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5127","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"}