Induced quadratic modules in $*$-algebras

Details Induced quadratic modules in $*$-algebras Induced quadratic modules in $*$-algebras

2012-01-06

arxiv.org/abs/1201.1374v2

Mathematics

Algebraic Geometry

Scientific paper

Positivity in $\ast$-algebras can be defined either algebraically, by quadratic modules, or analytically, by $\ast$-representations. By the induction procedure for $\ast$-representations we can lift the analytical notion of positivity from a $\ast$-subalgebra to the entire $\ast$-algebra. The aim of this paper is to define and study the induction procedure for quadratic modules. The main question is when a given quadratic module on the $\ast$-algebra is induced from its intersection with the $\ast$-subalgebra. This question is very hard even for the smallest quadratic module (i.e. the set of all sums of hermitian squares) and will be answered only in very special cases.

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