{"paper":{"title":"Factorizations, classifying complements problem and deformation maps for Lie-Yamaguti algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Apurba Das","submitted_at":"2026-05-25T08:29:22Z","abstract_excerpt":"A Lie-Yamaguti algebra is a non-associative algebraic structure that generalizes both Lie algebras and Lie triple systems. We first consider the factorization problem for Lie-Yamaguti algebras that essentially related to the bicrossed product of Lie-Yamaguti algebras. Next, given an inclusion $\\mathfrak{g} \\subset E$ of Lie-Yamaguti algebras and a strong $\\mathfrak{g}$-complement $\\mathfrak{h}$, we describe and classify all $\\mathfrak{g}$-complements in $E$. In particular, we show that any other $\\mathfrak{g}$-complement in $E$ is isomorphic to $\\mathfrak{h}$ by some deformation map $r: \\mathf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25576","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25576/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}