A Representation Theorem for Archimedean Quadratic Modules on $*$-Rings
[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.
[发布日期] [发布机构]
[效力级别] [学科分类] 数学(综合)
[关键词] Ordered rings with involution;$C^ast$-algebras and their representations;noncommutative convexity theory;real algebraic geometry [时效性]