{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TQZSVZKBJ77E3FD2ZFMUSBPAD5","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":"f04fa1f5ec1c5435adce0e55a0c0c1fefb6e38eec05ce364866878b7c4e6dbb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-01-27T11:13:53Z","title_canon_sha256":"3cc1829e906da8b50b669bc5eb1d3a3cb5172bbfab760067873ea7b63b5e2c3c"},"schema_version":"1.0","source":{"id":"0901.4221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4221","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4221v3","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4221","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"TQZSVZKBJ77E","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TQZSVZKBJ77E3FD2","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TQZSVZKB","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:e07c3aa94cca6a3f99e4190525279f019ffb995a34e7525ab589d81004d26359","target":"graph","created_at":"2026-05-18T04:40:00Z","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":"In this paper we study the tensor category structure of the module category of the restricted quantum enveloping algebra associated to $\\mathfrak{sl}_2$. Indecomposable decomposition of all tensor products of modules over this algebra is completely determined in explicit formulas. As a by-product, we show that the module category of the restricted quantum enveloping algebra associated to $\\mathfrak{sl}_2$ is not a braided tensor category.","authors_text":"Hiroki Kondo, Yoshihisa Saito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-01-27T11:13:53Z","title":"Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to $\\boldsymbol{\\mathfrak{sl}_2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4221","kind":"arxiv","version":3},"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":"sha256:444942953959e19cc2788bd5ed3185aa6df19a0411cfd6b49ef2d5b7644f8755","target":"record","created_at":"2026-05-18T04:40:00Z","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":"f04fa1f5ec1c5435adce0e55a0c0c1fefb6e38eec05ce364866878b7c4e6dbb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-01-27T11:13:53Z","title_canon_sha256":"3cc1829e906da8b50b669bc5eb1d3a3cb5172bbfab760067873ea7b63b5e2c3c"},"schema_version":"1.0","source":{"id":"0901.4221","kind":"arxiv","version":3}},"canonical_sha256":"9c332ae5414ffe4d947ac9594905e01f5cc8e57d6ead48807a631d55a9a2e48b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c332ae5414ffe4d947ac9594905e01f5cc8e57d6ead48807a631d55a9a2e48b","first_computed_at":"2026-05-18T04:40:00.792962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:00.792962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WzahCB2ACJaW3DD4Zhd61GbzitulMSOjj2PKphUbFWRNhhM6Atpr5jV2gl2jrqYPTNQgn8Sc8VyXk5P8b2G2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:00.793566Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:444942953959e19cc2788bd5ed3185aa6df19a0411cfd6b49ef2d5b7644f8755","sha256:e07c3aa94cca6a3f99e4190525279f019ffb995a34e7525ab589d81004d26359"],"state_sha256":"076870c857b99a703edf1f412421d2177ca0af78f26d81666bac91cdc6c4d3b3"}