Noncommutative Positivstellensätze for pairs representation-vector
Cimprič, Jaka
V običajnem pristopu k nekomutativni realni algebraični geometriji za asociativno ▫$\ast$▫-algebro ▫$\mathcal{A}$▫ so točke kar ▫$\ast$▫-reprezentacije algebre ▫$\mathcal{A}$▫. Alternativen pristop, ...ki ga proučujemo v tem članku, je, da za točke vzamemo pare ▫$(\pi,v)$▫, kjer je ▫$\pi$▫ ▫$ast$▫-reprezenacija algebre ▫$\mathcal{A}$▫ in ▫$v$▫ element reprezentacijskega prostora. Pri matričnih polinomih in prostih ▫$\ast$▫-algebrah se lahko omejimo na lepe točke, za splošne ▫$\ast$▫-algebre pa moramo vzeti vse točke.
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