{"paper":{"title":"Lowest positive almost central elements of $U_q(sl^{(1)}(n|n))$ $(n\\geq 2)$, $U_q(sl^{(2)}(2n|2n))$ $(n\\geq 2)$ and $U_q(sl^{(4)}(2n+1|2n+1))$ $(n\\geq 1)$ and their multi-parameter quantum affine superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hiroyuki Yamane","submitted_at":"2018-09-10T09:57:30Z","abstract_excerpt":"Let $\\pi:sl(n|n)\\to A(n-1,n-1)$ be the natural epimorphism of Lie superalgebra. Then $\\dim\\ker\\pi=1$. Let $\\pi^{(t)}:sl^{(t)}(n|n)\\to A^{(t)}(n-1,n-1)$ be the natural epimorphism, where $t=1,2,4$. Let $\\{e_k|k\\in{\\mathbb{Z}}\\}$ be the basis of $\\ker\\pi^{(t)}$ with $e_k\\in sl^{(t)}(n|n)_{(a_tk+b_t)\\delta}$, where $(a_1,b_1)=(1,0)$, $(a_2,b_2)=(2,-1)$ and $(a_4,b_4)=(4,-2)$. The main result of this paper is to explicitly describe an element of $U_q(sl^{(t)}(n|n))$ (and its multi-parameter version) corresponding to $e_1$ (i.e., $k=1$). As for $U_q(sl^{(1)}(n|n))$ (i.e., $t=1$), the author had alr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03223","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"}