{"paper":{"title":"On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitri Panyushev, Oksana Yakimova","submitted_at":"2013-12-06T14:27:51Z","abstract_excerpt":"For any involution $\\sigma$ of a semisimple Lie algebra $\\mathfrak g$, one constructs a non-reductive Lie algebra $\\mathfrak k$, which is called a $\\mathbb Z_2$-contraction of $\\mathfrak g$. In this paper, we attack the problem of describing maximal commutative subalgebras of the Poisson algebra $S(\\mathfrak k)$. This is closely related to the study of the coadjoint representation of $\\mathfrak k$ and the set, $\\mathfrak k^*_{reg}$, of the regular elements of $\\mathfrak k^*$. By our previous results, in the context of $\\mathbb Z_2$-contractions, the argument shift method provides maximal commu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1872","kind":"arxiv","version":1},"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"}