{"paper":{"title":"Centralizing Traces and Lie Triple Isomorphisms on Triangular 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, Xinfeng Liang, Zhankui Xiao","submitted_at":"2013-01-10T07:57:00Z","abstract_excerpt":"Let $\\mathcal{T}$ be a triangular algebra over a commutative ring $\\mathcal{R}$ and $\\mathcal{Z(T)}$ be the center of $\\mathcal{T}$. Suppose that ${\\mathfrak q}\\colon \\mathcal{T}\\times \\mathcal{T}\\longrightarrow \\mathcal{T}$ is an $\\mathcal{R}$-bilinear mapping and that ${\\mathfrak T}_{\\mathfrak q}\\colon: \\mathcal{T}\\longrightarrow \\mathcal{T}$ is a trace of $\\mathfrak{q}$. We describe the form of ${\\mathfrak T}_{\\mathfrak q}$ satisfying the condition $[{\\mathfrak T}_{\\mathfrak q}(T), T]\\in \\mathcal{Z(T)}$ for all $T\\in \\mathcal{T}$. The question of when ${\\mathfrak T}_{\\mathfrak q}$ has the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2043","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"}