{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G4IZN47ZR35F2JS4YL3GMZX6J3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d4d3e394f5c47d224960e6b292867cf600b933e8521ae5275b745876aea1be22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-26T00:14:16Z","title_canon_sha256":"a011764bd1f60c98a175219e8b6d10d9f139ae543455f74a89563f0e2dc2640c"},"schema_version":"1.0","source":{"id":"1403.6536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6536","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6536v1","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6536","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"G4IZN47ZR35F","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4IZN47ZR35F2JS4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4IZN47Z","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d7d38b8e939459de608e3a19acc796295d2823069c4c07c4461d60fa698a3c34","target":"graph","created_at":"2026-05-18T02:55:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study algebra endomorphisms and derivations of some localized down-up algebras $\\A$. First, we determine all the algebra endomorphisms of $\\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\\A$ is an algebra automorphism if $r^{m}s^{n}=1$ implies $m=n=0$. When $r=s^{-1}=q$ is not a root of unity, we give a criterion for an algebra endomorphism of $\\A$ to be an algebra automorphism. In either case, we are able to determine the algebra automorphism group for $\\A$. We also show that each surjective algebra endomorphism of the down-up algebra $A(r+s, -rs)$ is a","authors_text":"Xin Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-26T00:14:16Z","title":"Algebra endomorphisms and Derivations of Some Localized Down-Up Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6536","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:57849f26915165afbe6ddb30972b59752f2a5af0f103f1d5793eb822abc7ff07","target":"record","created_at":"2026-05-18T02:55:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d4d3e394f5c47d224960e6b292867cf600b933e8521ae5275b745876aea1be22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-26T00:14:16Z","title_canon_sha256":"a011764bd1f60c98a175219e8b6d10d9f139ae543455f74a89563f0e2dc2640c"},"schema_version":"1.0","source":{"id":"1403.6536","kind":"arxiv","version":1}},"canonical_sha256":"371196f3f98efa5d265cc2f66666fe4eddc13211a3c9b09eb7a85f2f6cce57a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371196f3f98efa5d265cc2f66666fe4eddc13211a3c9b09eb7a85f2f6cce57a4","first_computed_at":"2026-05-18T02:55:28.679449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:28.679449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0Csk6c44yuhd7HKYsoYEmOxVr/sHFqkXnG7CV6de9XbhyO/8Jiw+R+2d9h9f6Tjrs5Be862dotA0rvUjC6KCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:28.680031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57849f26915165afbe6ddb30972b59752f2a5af0f103f1d5793eb822abc7ff07","sha256:d7d38b8e939459de608e3a19acc796295d2823069c4c07c4461d60fa698a3c34"],"state_sha256":"1cbaaaabd9eb05b0699c9c5cf7825faf201c919a8adf7e631e3d3f6eb35c73da"}