On Positive Deformations of *-Algebras

Details On Positive Deformations of *-Algebras On Positive Deformations of *-Algebras

1999-10-21

arxiv.org/abs/math/9910112v1

Mathematics

Quantum Algebra

LaTeX2e, 11pages. Contribution to the CMF 1999

Scientific paper

Motivated by deformation quantization we consider $^*$-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the $^*$-involution and discuss a cohomological description in terms of a Hermitian Hochschild cohomology. As an ordered ring allows for a meaningful definition of positive functionals and as the formal power series with coefficients in an ordered ring are again an ordered ring we define a deformation to be positive if any positive linear functional of the undeformed algebra can be deformed into a positive linear functional of the deformed algebra. We discuss various examples and prove in particular that star products on symplectic manifolds are positive deformations.

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