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In this paper, we suppose that $\\Phi:\\mathcal{A}\\to\\mathcal{A}$ satisfies $$\\Phi(A\\diamond B)=\\Phi(A)\\diamond B+A\\diamond\\Phi(B)$$ where $A\\diamond B = A^{*}B - B^{*}A$ for all $A,B\\in\\mathcal{A}$ .We will show that if $\\Phi(\\alpha \\frac{I}{2})$ is self-adjoint for $\\alpha\\in\\{1,i\\}$ then $\\Phi$ is additive $\\ast$-derivation."},"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":"1905.07577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-18T11:43:28Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"61b9ac6163090a336ddd5805f780081237090f9f4fa2c854a25ebd464abdf823","abstract_canon_sha256":"033a29ab90df45827dad72c167308e49550124cd634c5755e73458886b909def"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:49.228028Z","signature_b64":"cjWOAdk7Eaxnez8F6FN8+8GDXAEA77AJzN732keMPuc1FQVUpH+5rY0Y5BR+WHCk3vRdsNBjdAesDxsnvKKsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9446dec8a505a68e1b525c3be66e40ef92d94c6cf33328f819035aff4ab79630","last_reissued_at":"2026-05-17T23:45:49.227372Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:49.227372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Linear New Product $A^*B-B^*A$ Derivations on $\\ast$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Ali Taghavi, Mehran Razeghi","submitted_at":"2019-05-18T11:43:28Z","abstract_excerpt":"Let $\\mathcal{A}$ be a prime $\\ast$-algebra. 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