{"paper":{"title":"Induced quadratic modules in $*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RA","math.RT"],"primary_cat":"math.AG","authors_text":"Jaka Cimpric, Yurii Savchuk","submitted_at":"2012-01-06T09:01:54Z","abstract_excerpt":"Positivity in $\\ast$-algebras can be defined either algebraically, by quadratic modules, or analytically, by $\\ast$-representations. By the induction procedure for $\\ast$-representations we can lift the analytical notion of positivity from a $\\ast$-subalgebra to the entire $\\ast$-algebra. The aim of this paper is to define and study the induction procedure for quadratic modules. The main question is when a given quadratic module on the $\\ast$-algebra is induced from its intersection with the $\\ast$-subalgebra. This question is very hard even for the smallest quadratic module (i.e. the set of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1374","kind":"arxiv","version":3},"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"}