{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AMXRPLRR3LZTWKRCXRDI4OJ5F6","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":"d324e9e935e121286c591ad4bf5ceed9c693c12aa34fb0b10bb0c35af0814a17","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-07-07T09:17:04Z","title_canon_sha256":"30cf2c45b78f7b29e26ffe3151e8fae9e5b37386683d69997658d9687835dc33"},"schema_version":"1.0","source":{"id":"1707.02091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02091","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02091v2","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02091","created_at":"2026-05-18T00:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"AMXRPLRR3LZT","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMXRPLRR3LZTWKRC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMXRPLRR","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:a0103f08d8b1827cd1a1ef4a170fa307a79d48ff1bb958e9ce688e3a1c03c6c4","target":"graph","created_at":"2026-05-18T00:07:43Z","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":"Let $\\mathcal{D}$ be the Drinfeld double of $\\mathcal{FK}_3\\#\\Bbbk{\\mathbb S}_3$. The simple $\\mathcal{D}$-modules were described in arXiv:1409.0438. In the present work, we describe the indecomposable summands of the tensor product between them. We classify the extensions of the simple modules and show that $\\mathcal{D}$ is of wild representation type. We also investigate the projective modules and their tensor products.","authors_text":"Barbara Pogorelsky, Cristian Vay","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-07-07T09:17:04Z","title":"On the representation theory of the Drinfeld double of the Fomin-Kirillov algebra $\\mathcal{FK}_3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02091","kind":"arxiv","version":2},"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":"sha256:84c702b530048eeb3de88a876232554d76cf1c1902a69aa3032a2909401bced0","target":"record","created_at":"2026-05-18T00:07:43Z","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":"d324e9e935e121286c591ad4bf5ceed9c693c12aa34fb0b10bb0c35af0814a17","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-07-07T09:17:04Z","title_canon_sha256":"30cf2c45b78f7b29e26ffe3151e8fae9e5b37386683d69997658d9687835dc33"},"schema_version":"1.0","source":{"id":"1707.02091","kind":"arxiv","version":2}},"canonical_sha256":"032f17ae31daf33b2a22bc468e393d2fba57f6f608244a295934502265ca9024","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"032f17ae31daf33b2a22bc468e393d2fba57f6f608244a295934502265ca9024","first_computed_at":"2026-05-18T00:07:43.824174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:43.824174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EvWX8jJA5Vocs2Ra8XnfPpKhLkSzTZbtmvXAOEBh3UVfP9yY8eSsBFqxqvlDtbImV+cDN9bMSqd/C6pr3+oKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:43.824849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84c702b530048eeb3de88a876232554d76cf1c1902a69aa3032a2909401bced0","sha256:a0103f08d8b1827cd1a1ef4a170fa307a79d48ff1bb958e9ce688e3a1c03c6c4"],"state_sha256":"8c48c9795b406f4e4e115f1b2a08d96b85e5758656ca5d0a55476078cfde1d7e"}