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Next, we show that the tame tilted algebras are precisely those tilted algebras $A$ with the property that for each generic root $\\dd$ of $A$ and each indecomposable irreducible component $C \\subseteq \\module(A,\\dd)$, the moduli space $\\M(C)^{ss}_{\\theta}$ is either a point or just $\\mathbb P^1$ whenever $\\theta$ is an integral weight for which $C^s_{\\"},"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":"1109.2915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-13T20:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"198d8d86da13a842a09d24f52cde68db587ac8891c8b52ee696887b5e3ed51a8","abstract_canon_sha256":"a5b60faf1f61af1e318be9f1925341ddaa05419e634b2851565487f054ebf7a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:06.726576Z","signature_b64":"ZFmUhzvtlq20Dtbbmms+c0WCl8G8mOtha9apFTjkjZmrP490rbeWwz3nFHJ3wS5VnxVCcUg/hFGHmuYaskmrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58e101a228d0dbb31b6b924df06d3e67bad6fc5e872aeed527db1a1b61f60229","last_reissued_at":"2026-05-18T04:13:06.726112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:06.726112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the invariant theory for tame tilted algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Calin Chindris","submitted_at":"2011-09-13T20:26:20Z","abstract_excerpt":"We show that a tilted algebra $A$ is tame if and only if for each generic root $\\dd$ of $A$ and each indecomposable irreducible component $C$ of $\\module(A,\\dd)$, the field of rational invariants $k(C)^{\\GL(\\dd)}$ is isomorphic to $k$ or $k(x)$. Next, we show that the tame tilted algebras are precisely those tilted algebras $A$ with the property that for each generic root $\\dd$ of $A$ and each indecomposable irreducible component $C \\subseteq \\module(A,\\dd)$, the moduli space $\\M(C)^{ss}_{\\theta}$ is either a point or just $\\mathbb P^1$ whenever $\\theta$ is an integral weight for which $C^s_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2915","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.2915","created_at":"2026-05-18T04:13:06.726177+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.2915v1","created_at":"2026-05-18T04:13:06.726177+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2915","created_at":"2026-05-18T04:13:06.726177+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDQQDIRI2DN3","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDQQDIRI2DN3GG3L","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDQQDIRI","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6","json":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6.json","graph_json":"https://pith.science/api/pith-number/LDQQDIRI2DN3GG3LSJG7A3J6M6/graph.json","events_json":"https://pith.science/api/pith-number/LDQQDIRI2DN3GG3LSJG7A3J6M6/events.json","paper":"https://pith.science/paper/LDQQDIRI"},"agent_actions":{"view_html":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6","download_json":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6.json","view_paper":"https://pith.science/paper/LDQQDIRI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.2915&json=true","fetch_graph":"https://pith.science/api/pith-number/LDQQDIRI2DN3GG3LSJG7A3J6M6/graph.json","fetch_events":"https://pith.science/api/pith-number/LDQQDIRI2DN3GG3LSJG7A3J6M6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6/action/storage_attestation","attest_author":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6/action/author_attestation","sign_citation":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6/action/citation_signature","submit_replication":"https://pith.science/pith/LDQQDIRI2DN3GG3LSJG7A3J6M6/action/replication_record"}},"created_at":"2026-05-18T04:13:06.726177+00:00","updated_at":"2026-05-18T04:13:06.726177+00:00"}