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Then in this paper, we first introduce the definition of braided Hom-Lie algebras and show that each monoidal Hom-algebra in $^{H}_{H}\\mathcal{HYD}$ gives rise to a braided Hom-Lie algebra. Second, we prove that if $(A,\\beta)$ is a sum of two $H$-commutative monoidal Hom-subalgebras, then the commutator Hom-ideal $[A,A]$ of $A$ is nilpotent. Also, we study the central invariant of braided Hom-Lie algebras as a generalization of generalized Lie algebras. Finally, we ob"},"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":"1902.06252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-17T12:58:03Z","cross_cats_sorted":[],"title_canon_sha256":"2b89ef505fda4241312986748a30f5fb4960eca0ef37e364dc755d51eae49b87","abstract_canon_sha256":"0ef3dc5e7830e077f6b61f1b1b0c2283a499d3087f0a5f871aa84f153c509147"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:46.090248Z","signature_b64":"sOhZqF3yh/p+TRTxBsOSaFy5aURt0w3LxepIQZ8Ygcjy9DuzPEXEqoqMMrm0krEqdGkx0v4rGXdcnzIkKadkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6fa9cc4fd517bd678b3887db42c666d8818d16dbdb4e9ec842a6b4558bd8fdd","last_reissued_at":"2026-05-17T23:53:46.089633Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:46.089633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central invariants and enveloping algebras of braided Hom-Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Shengxiang Wang, Shuangjian Guo, Xiaohui Zhang","submitted_at":"2019-02-17T12:58:03Z","abstract_excerpt":"Let $(H,\\alpha)$ be a monoidal Hom-Hopf algebra and $^{H}_{H}\\mathcal{HYD}$ the Hom-Yetter-Drinfeld category over $(H,\\alpha)$. 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