{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LPDLIJOCE3AYO4F7NL6QCWXZTX","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":"ad83f7d72d473afab7d8f9f93906ec3618b00decebed191ee69f7b5baa227aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-28T13:28:19Z","title_canon_sha256":"50c650ef9aab565d35f6838597224054c9f4df5ad2b6a7d18f840ea515850f54"},"schema_version":"1.0","source":{"id":"1704.08921","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08921","created_at":"2026-05-18T00:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08921v2","created_at":"2026-05-18T00:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08921","created_at":"2026-05-18T00:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"LPDLIJOCE3AY","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LPDLIJOCE3AYO4F7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LPDLIJOC","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:243ce66013cca5e6bfe163fe629882c72a401d27d9d95cf4c74e1984a7ebb872","target":"graph","created_at":"2026-05-18T00:22:39Z","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":"We study a mixed tensor product $\\mathbf{3}^{\\otimes m} \\otimes \\mathbf{\\overline{3}}^{\\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\\ell(2|1)$, whenever $q$ is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective $U_{q} s\\ell(2|1)$-module with the generating modules $\\mathbf{3}$ and $\\mathbf{\\overline{3}}$ are obtained. The centralizer of $U_{q} s\\ell(2|1)$ on the chain is calculated. It is shown to be the quotient $\\mathscr{X}_{m,n}$ of the quantum walled Brauer algebra. The structure of projective ","authors_text":"A.M. Kiselev, D.V. Bulgakova, I.Yu. Tipunin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-28T13:28:19Z","title":"Bimodule structure of the mixed tensor product over $U_{q} s\\ell(2|1)$ and quantum walled Brauer algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08921","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":"sha256:7181b891b18f33ca5513d3c55e3310b34a03d9ce67ba733b52278d090fdf8742","target":"record","created_at":"2026-05-18T00:22:39Z","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":"ad83f7d72d473afab7d8f9f93906ec3618b00decebed191ee69f7b5baa227aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-04-28T13:28:19Z","title_canon_sha256":"50c650ef9aab565d35f6838597224054c9f4df5ad2b6a7d18f840ea515850f54"},"schema_version":"1.0","source":{"id":"1704.08921","kind":"arxiv","version":2}},"canonical_sha256":"5bc6b425c226c18770bf6afd015af99dd5930991c255ab5ca7c700f592e1819d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bc6b425c226c18770bf6afd015af99dd5930991c255ab5ca7c700f592e1819d","first_computed_at":"2026-05-18T00:22:39.923478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:39.923478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uuOm2IlUOhEjCBDQnOjItFej1vysXyxzYqMcQ053ZxHwliM0sp4cOIQayhD1vB47n/MVBI+67wu42iXlitcoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:39.923916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08921","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7181b891b18f33ca5513d3c55e3310b34a03d9ce67ba733b52278d090fdf8742","sha256:243ce66013cca5e6bfe163fe629882c72a401d27d9d95cf4c74e1984a7ebb872"],"state_sha256":"0e4973a87d0b1a189e932f800eea6a734cebf68c0348f9ea12298f7e2b469f92"}