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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.03223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-10T09:57:30Z","cross_cats_sorted":[],"title_canon_sha256":"ff0d80a49bc2981289793fc32fc44c2efb0cbd9a0fdd273862cbda4a5b858277","abstract_canon_sha256":"723114585d45407427513e1a5d50def1fc4df279758acaef5efe10290f8e49f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:09.594110Z","signature_b64":"tmnha30wQjUgFBR5F36drB5REKKIiog4mJrEe4AI3ktw9JraND7kVJZ/6k+6etiV2BY5c3n0ZDXiwckYfcN8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c345d1b61056f7c216513214efb87896a7e15f3db670bf1f4ca4a48b4dbd918","last_reissued_at":"2026-05-18T00:06:09.593473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:09.593473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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