{"paper":{"title":"Commuting Traces and Lie Isomorphisms on Generalized Matrix Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.RA","authors_text":"Feng Wei, Zhankui Xiao","submitted_at":"2012-10-12T12:13:43Z","abstract_excerpt":"Let $\\mathcal{G}$ be a generalized matrix algebra over a commutative ring $\\mathcal{R}$, ${\\mathfrak q}\\colon \\mathcal{G}\\times\\mathcal{G}\\longrightarrow \\mathcal{G}$ be an $\\mathcal{R}$-bilinear mapping and ${\\mathfrak T}_{\\mathfrak q}\\colon:\\mathcal{G}\\longrightarrow \\mathcal{G}$ be a trace of $\\mathfrak{q}$. We describe the form of ${\\mathfrak T}_{\\mathfrak q}$ satisfying the condition ${\\mathfrak T}_{\\mathfrak q}(G)G=G{\\mathfrak T}_{\\mathfrak q}(G)$ for all $G\\in \\mathcal{G}$. The question of when ${\\mathfrak T}_{\\mathfrak q}$ has the proper form is considered. Using the aforementioned tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3488","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"}