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Given a finite dimensional ${\\mathfrak g}$-module $U$, its nilpotency series $ 0\\subset U({\\mathfrak n}^1)\\subset\\cdots\\subset U({\\mathfrak n}^m)=U$ is defined so that $U({\\mathfrak n}^1)$ is the 0-weight space of ${\\mathfrak n}$ in $U$, $U({\\mathfrak n}^2)/U({\\mathfrak n}^1)$ is the 0-weight space of ${\\mathfrak n}$ in $U/U({\\mathfrak n}^1)$, and so on. We say that $U$ is linked if each factor of it"},"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":"1407.8125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-30T16:57:20Z","cross_cats_sorted":[],"title_canon_sha256":"9080c0d6f9ef63044d683b3e072e33bc82e70692936f7f2db764d9fcb037779b","abstract_canon_sha256":"ebafd89b00477746437f9c95b60293ab0621a9eca7d6f38705b751a7fa09c801"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.854579Z","signature_b64":"D7l+v49CXXa5+iajY/+z8jzmvNo3xMOnCL/9mYuGH/dnoXgEW81Y1Euo1to6oUipWhVvpleZoxTzsdfwMGQsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21613e73c72f681de0a872e6cbe7b2a5616cfea8586a10b93f4e874672bbee1c","last_reissued_at":"2026-05-18T02:38:52.854243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.854243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of linked indecomposable modules of a family of solvable Lie algebras over an arbitrary field of characteristic 0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, Leandro Cagliero","submitted_at":"2014-07-30T16:57:20Z","abstract_excerpt":"Let ${\\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\\mathfrak r}$ and nilpotent radical ${\\mathfrak n}=[{\\mathfrak g},{\\mathfrak r}]$. Given a finite dimensional ${\\mathfrak g}$-module $U$, its nilpotency series $ 0\\subset U({\\mathfrak n}^1)\\subset\\cdots\\subset U({\\mathfrak n}^m)=U$ is defined so that $U({\\mathfrak n}^1)$ is the 0-weight space of ${\\mathfrak n}$ in $U$, $U({\\mathfrak n}^2)/U({\\mathfrak n}^1)$ is the 0-weight space of ${\\mathfrak n}$ in $U/U({\\mathfrak n}^1)$, and so on. 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