On Positive Deformations of *-Algebras

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dc.creatorBursztyn, Henrique
dc.creatorWaldmann, Stefan
dc.date1999-10-21
dc.date.accessioned2026-07-07T05:31:14Z
dc.date.available2026-07-07T05:31:14Z
dc.descriptionMotivated 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.
dc.descriptionLaTeX2e, 11pages. Contribution to the CMF 1999
dc.identifierhttps://arxiv.org/abs/math/9910112
dc.identifierhttp://arxiv.org/abs/math/9910112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79269
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.titleOn Positive Deformations of *-Algebras
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