On Positive Deformations of *-Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.math/9910112,
title = {On Positive Deformations of *-Algebras},
author = {Henrique Bursztyn and Stefan Waldmann},
journal= {arXiv preprint arXiv:math/9910112},
year = {2007}
}
Comments
LaTeX2e, 11pages. Contribution to the CMF 1999