{"paper":{"title":"Invariant Subspaces of Nilpotent Linear Operators. I","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Claus Michael Ringel, Markus Schmidmeier","submitted_at":"2006-08-28T02:19:21Z","abstract_excerpt":"Let $k$ be a field. We consider triples $(V,U,T)$, where $V$ is a finite dimensional $k$-space, $U$ a subspace of $V$ and $T \\:V \\to V$ a linear operator with $T^n = 0$ for some $n$, and such that $T(U) \\subseteq U$. Thus, $T$ is a nilpotent operator on $V$, and $U$ is an invariant subspace with respect to $T$.\n  We will discuss the question whether it is possible to classify these triples. These triples $(V,U,T)$ are the objects of a category with the Krull-Remak-Schmidt property, thus it will be sufficient to deal with indecomposable triples. Obviously, the classification problem depends on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608666","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}