{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z6LVFUZKF7QL3CMUBPZUCTL4OW","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":"10ae6032c4bbac8da0abc0bc34bfeb45928730f1ee23faeb8ac72eef7492a26f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-19T21:11:46Z","title_canon_sha256":"4652f59407180278eed9240f97386a38be238920ebc589f5eee55f5875bac037"},"schema_version":"1.0","source":{"id":"1308.4175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4175","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4175v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4175","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"Z6LVFUZKF7QL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z6LVFUZKF7QL3CMU","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z6LVFUZK","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:b732d7b96ec2f0dcc7706ae1b4888dcddbbe61035bfbf78ce57c77d695d363e4","target":"graph","created_at":"2026-05-18T03:15:33Z","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":"Given a central simple algebra $\\mathfrak{g}$ and a Galois extension of base rings $S/R$, we show that the maximal ideals of twisted $S/R$-forms of the algebra of currents $\\mathfrak{g}(R)$ are in natural bijection with the maximal ideals of $R$. When $\\mathfrak{g}$ is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of $\\mathfrak{g}(R)$.","authors_text":"Arturo Pianzola, Michael Lau","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-19T21:11:46Z","title":"Maximal ideals and representations of twisted forms of algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4175","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":"sha256:339173d184a155c7121ef8ce4d51eb148cd3f468dc8719654e65093fb05796a8","target":"record","created_at":"2026-05-18T03:15:33Z","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":"10ae6032c4bbac8da0abc0bc34bfeb45928730f1ee23faeb8ac72eef7492a26f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-19T21:11:46Z","title_canon_sha256":"4652f59407180278eed9240f97386a38be238920ebc589f5eee55f5875bac037"},"schema_version":"1.0","source":{"id":"1308.4175","kind":"arxiv","version":1}},"canonical_sha256":"cf9752d32a2fe0bd89940bf3414d7c75887355ea81015972f669228859e3792a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf9752d32a2fe0bd89940bf3414d7c75887355ea81015972f669228859e3792a","first_computed_at":"2026-05-18T03:15:33.556506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:33.556506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIPkSxSzYl2vcBnrGDw5/nLA5u2P//MZI6W0vS9IXVYOI7iKxVb/WnZxJZ/R/jKcM0hJD2q3VKcENQezCu/NAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:33.557231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339173d184a155c7121ef8ce4d51eb148cd3f468dc8719654e65093fb05796a8","sha256:b732d7b96ec2f0dcc7706ae1b4888dcddbbe61035bfbf78ce57c77d695d363e4"],"state_sha256":"fe85661b33a2e753a0e7c5c5015f036498359ca824833e7ab292cec9a95e4c8c"}