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We describe the set of all $*$-polynomial identities for $\\mathcal{A}$ with the involution defined by the reflection of second diagonal."},"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":"1810.12362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-29T19:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"36d9091277ac73263870b259bad6136751af9614b4d361e90f1837f294840530","abstract_canon_sha256":"b042e77b714e544dcd987a237de22a7dce20b8a8d0ff5437a80b1e722bd3fa00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.919354Z","signature_b64":"dcJZXKIn99N6wpkJXsY+I/aqPK3FmorZhOQmk0uHAf3N91rmP4i8Gt+xu/6jRvEnxex3u/H3V8w6LwaHG6NKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c01f873db841c414babb1f5117a54e84f6675fbbe72befe07555ae52937127","last_reissued_at":"2026-05-18T00:02:02.918764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.918764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"*-polynomial identities of 4x4 upper triangular matrices with the reflection involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ronald Ismael Quispe Urure","submitted_at":"2018-10-29T19:10:51Z","abstract_excerpt":"Let $UT_4(F)$ be $4\\times 4$ upper triangular matrix algebra over a field $F$ of characteristic zero and let $\\mathcal{A}$ be the subalgebra of $UT_4(F)$ linearly generated by $\\{\\mathbf{e}_{ij}:1 \\leq i\\leq j \\leq 4 \\} \\setminus \\mathbf{e}_{23}$ where $\\{\\mathbf{e}_{ij} : 1 \\leq i\\leq j \\leq 4\\}$ is the standard basis of $UT_4(F)$. 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