{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HM2JBR6CWFDNH7LXNVSVMWFRJH","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":"40670f968220b5d7f96ea0f7d3b54e7a9f16140956a26b0c9978732e8b8479f3","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-02-16T19:56:24Z","title_canon_sha256":"c3cce7cb0a916075b247db6ac3a44e65ca92e19807a9e5f19723a9af73f0637b"},"schema_version":"1.0","source":{"id":"1702.05133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05133","created_at":"2026-05-18T00:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05133v1","created_at":"2026-05-18T00:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05133","created_at":"2026-05-18T00:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"HM2JBR6CWFDN","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HM2JBR6CWFDNH7LX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HM2JBR6C","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:ecc22942cecdc772f3b7f2e0eb83a96f3a9c32ca835d431aafd543108f151313","target":"graph","created_at":"2026-05-18T00:50:34Z","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 article we construct three explicit natural subgroups of the Brauer-Picard group of the category of representations of a finite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes into an ordered product of these subgroups, somewhat similar to a Bruhat decomposition.\n  Our construction returns for any Hopf algebra three types of braided autoequivalences and correspondingly three families of invertible bimodule categories. This gives examples of so-called (2-)Morita equivalences and defects in topological field theories. We have a closer look at the case of quantum ","authors_text":"Jan Priel, Simon D. Lentner","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-02-16T19:56:24Z","title":"Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05133","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":"sha256:6227a49ce48828e014376992c72abc2c0450f0b8e95d75ea718e0eefcfde3a06","target":"record","created_at":"2026-05-18T00:50:34Z","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":"40670f968220b5d7f96ea0f7d3b54e7a9f16140956a26b0c9978732e8b8479f3","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-02-16T19:56:24Z","title_canon_sha256":"c3cce7cb0a916075b247db6ac3a44e65ca92e19807a9e5f19723a9af73f0637b"},"schema_version":"1.0","source":{"id":"1702.05133","kind":"arxiv","version":1}},"canonical_sha256":"3b3490c7c2b146d3fd776d655658b149e62c04e6cba6dcae4c860ae72d5398c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b3490c7c2b146d3fd776d655658b149e62c04e6cba6dcae4c860ae72d5398c8","first_computed_at":"2026-05-18T00:50:34.773795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:34.773795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cMDio/cVRX2rcLaoGs9E1mxL+fzsMBBNMR0tLYHKGOaXU9ESZnGPy/TCnCVUEx07wC3Xy3RDhbvRV+zOyMyiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:34.774539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6227a49ce48828e014376992c72abc2c0450f0b8e95d75ea718e0eefcfde3a06","sha256:ecc22942cecdc772f3b7f2e0eb83a96f3a9c32ca835d431aafd543108f151313"],"state_sha256":"1e810dad36e2b55d13b0bc548af694d72cca5daef9f402b365a530c96a97c7eb"}