{"paper":{"title":"Another presentation for symplectic Steinberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Andrei Lavrenov","submitted_at":"2014-05-16T20:02:23Z","abstract_excerpt":"We solve a classical problem of centrality of symplectic $\\mathrm K_2$, namely we show that for an arbitrary commutative ring $R$, $l\\geq3$ the symplectic Steinberg group $\\mathrm{StSp}(2l,\\,R)$ as an extension of the elementary symplectic group $\\mathrm{Ep}(2l,\\,R)$ is a central extension. This allows to conclude that the explicit definition of symplectic $\\mathrm{K_2Sp}(2l,\\,R)$ as a kernel of this extension, i.e. as a group of non-elementary relations among symplectic transvections, coincides with the usual implicit definition via plus-construction. We proceed from van der Kallen's classica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4296","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"}