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arXiv · 0807.5020

A representation theorem for archimedean quadratic modules on *-rings

Jaka Cimpric
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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.

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Jaka Cimpric. 2008-07-31. A representation theorem for archimedean quadratic modules on *-rings. https://arxiv.org/abs/0807.5020

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