{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DW7RTNJSSF3EUD4GNK6OMBCDDJ","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":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa"},"schema_version":"1.0","source":{"id":"1610.00092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00092v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"DW7RTNJSSF3E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DW7RTNJSSF3EUD4G","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DW7RTNJS","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932","target":"graph","created_at":"2026-05-18T01:03:31Z","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 give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a Product Formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For k an algebraically closed field of characteristic p and G a finite group we prove an additive decomposition and a Product Formula for the cohomology algebra of a defect group of a block ideal of kG with coefficients in the source alg","authors_text":"Constantin-Cosmin Todea","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title":"Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00092","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:caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c","target":"record","created_at":"2026-05-18T01:03:31Z","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":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa"},"schema_version":"1.0","source":{"id":"1610.00092","kind":"arxiv","version":1}},"canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","first_computed_at":"2026-05-18T01:03:31.884443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.884443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kh6xA2875bBqmQInFEEZqkjl4F++wDzOOS+F2LLG2kLLVyqQAx17j56luE8ytPoZtlSKYQkYPp38DPjoMHCtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.884903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c","sha256:09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932"],"state_sha256":"eac5b6c99167b401dae52ff6677f38767cee49399d729559ce62616ec803c578"}