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This paper explores the algbaraic structures of generalized derivation superalgebra ${\\rm GDer}(g)$, compatatible generalized derivations algebra ${\\rm GDer}^{\\omega}(g)$, and their subvarieties such as quasiderivation superalgebra ${\\rm QDer}(g)$(${\\rm QDer}^{\\omega}(g)$), centroid ${\\rm Cent}(g)$ (${\\rm Cent}^{\\omega}(g)$) and quasicentroid ${\\rm QCent}(g)$ (${\\rm QCent}^{\\omega}(g)$). We prove that ${\\rm GDer}^{\\omega}(g) = {\\rm QDer}^{\\omega}(g) + {\\rm QCent}^{\\omega}(g)$. We also study the embedding quest"},"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":"2505.22966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-05-29T01:07:49Z","cross_cats_sorted":[],"title_canon_sha256":"db28bb7c72243bd7b5e72887c33f431846b1e8e0700b676b185df2ba2fe5c314","abstract_canon_sha256":"640544713dc217989861aaad95aed622cf4d2ff0b237e94e3b97535457fcdc7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:52.853276Z","signature_b64":"QQ/ttDttu1h45kPSMIoRuyS7H5LcdjwO3khcdW3WTEacLHXastgEjXidGmZ3suUjJtD6SS1wwodCeXL0M/tQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"879a4abf3e0385199780e05b2fe3121d057420084829e1284e61dddd016a6b9b","last_reissued_at":"2026-07-05T11:11:52.852750Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:52.852750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized derivations of Complex $\\omega$-Lie Superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jia Zhou","submitted_at":"2025-05-29T01:07:49Z","abstract_excerpt":"~Let $(g,~[-,-],~\\omega)$ be a finite-dimensional complex $\\omega$-Lie superalgebra. This paper explores the algbaraic structures of generalized derivation superalgebra ${\\rm GDer}(g)$, compatatible generalized derivations algebra ${\\rm GDer}^{\\omega}(g)$, and their subvarieties such as quasiderivation superalgebra ${\\rm QDer}(g)$(${\\rm QDer}^{\\omega}(g)$), centroid ${\\rm Cent}(g)$ (${\\rm Cent}^{\\omega}(g)$) and quasicentroid ${\\rm QCent}(g)$ (${\\rm QCent}^{\\omega}(g)$). We prove that ${\\rm GDer}^{\\omega}(g) = {\\rm QDer}^{\\omega}(g) + {\\rm QCent}^{\\omega}(g)$. 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