Abstract view
A Representation Theorem for Archimedean Quadratic Modules on $*$Rings


Published:20090301
Printed: Mar 2009
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.
We show that this theorem is a consequence of the
GelfandNaimark representation theorem for commutative $C^\ast$algebras.
A noncommutative version of GelfandNaimark theory was studied by
I. Fujimoto. We use his results to generalize
Jacobi's theorem to associative rings with involution.
MSC Classifications: 
16W80, 46L05, 46L89, 14P99 show english descriptions
Topological and ordered rings and modules [See also 06F25, 13Jxx] General theory of $C^*$algebras Other ``noncommutative'' mathematics based on $C^*$algebra theory [See also 58B32, 58B34, 58J22] None of the above, but in this section
16W80  Topological and ordered rings and modules [See also 06F25, 13Jxx] 46L05  General theory of $C^*$algebras 46L89  Other ``noncommutative'' mathematics based on $C^*$algebra theory [See also 58B32, 58B34, 58J22] 14P99  None of the above, but in this section
