Deformation Quantization of Hermitian Vector Bundles

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dc.creatorBursztyn, Henrique
dc.creatorWaldmann, Stefan
dc.date2000-09-18
dc.date.accessioned2026-07-07T04:37:27Z
dc.date.available2026-07-07T04:37:27Z
dc.descriptionMotivated by deformation quantization, we consider in this paper $^*$-algebras $\mathcal A$ over rings $\ring C = \ring{R}(i)$, where $\ring R$ is an ordered ring and $i^2 = -1$, and study the deformation theory of projective modules over these algebras carrying the additional structure of a (positive) $\mathcal A$-valued inner product. For $A=C^\infty(M)$, M a manifold, these modules can be identified with Hermitian vector bundles E over M. We show that for a fixed Hermitian star-product on M, these modules can always be deformed in a unique way, up to (isometric) equivalence. We observe that there is a natural bijection between the sets of equivalence classes of local Hermitian deformations of $C^\infty(M)$ and $Γ^\infty(\End(E))$ and that the corresponding deformed algebras are formally Morita equivalent, an algebraic generalization of strong Morita equivalence of $C^*$-algebras. We also discuss the semi-classical geometry arising from these deformations.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0009170
dc.identifierhttp://arxiv.org/abs/math/0009170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59957
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.titleDeformation Quantization of Hermitian Vector Bundles
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