A Representation Theorem for Archimedean Quadratic Modules on $*$-Rings

Canadian mathematical bulletin

关键词: Ordered rings with involution;    $C^ast$-algebras and their representations;    noncommutative convexity theory;    real algebraic geometry;   

DOI  :  10.4153/CMB-2009-005-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We present a new approach to noncommutative real algebraic geometrybased on the representation theory of $C^ast$-algebras.An important result in commutative real algebraic geometry isJacobi's representation theorem for archimedean quadratic moduleson commutative rings.We show that this theorem is a consequence of theGelfand--Naimark representation theorem for commutative $C^ast$-algebras.A noncommutative version of Gelfand--Naimark theory was studied byI. Fujimoto. We use his results to generalizeJacobi's theorem to associative rings with involution.

【 授权许可】

Unknown