{"paper":{"title":"G-set Theory and Applications in Lie Theory","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mehdi Nadjafikhah, Reza Aghayan","submitted_at":"2012-01-18T10:24:02Z","abstract_excerpt":"This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational\" and \"observability\" viewpoint. We specify set of all \"G-equivariant\" maps from a given Lie group G to the underlying manifold M, namely $G$-set, and also we introduce \"conjugacy\" in Lie group theory. The next goal of this paper is detailed analysis of the G-sets in connection with underlying transformation groups and providing a rigorous theoretical justification of \"G-sets\", when a group of transformations G acts on manifold M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3741","kind":"arxiv","version":4},"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"}