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- W2106685765 abstract "We present a new approach to noncommutative real algebraic geometry based on the representation theory of $C^ast$-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings, cite[Theorem 5]{jacobi}. We show that this theorem is a consequence of the Gelfand-Naimark representation theorem for commutative $C^ast$-algebras. A noncommutative version of Gelfand-Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution." @default.
- W2106685765 created "2016-06-24" @default.
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- W2106685765 date "2008-07-31" @default.
- W2106685765 modified "2023-09-26" @default.
- W2106685765 title "A representation theorem for archimedean quadratic modules on *-rings" @default.
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