Classification and Reduction of Homogeneous Star Products

2025/07/03 by Dippell, Marvin, Esposito, Chiara, Schnitzer, Jonas
#53D17 #53D20 #53D55 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2507.02820

Abstract

We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible with (coisotropic) reduction. This implies that quantization commutes with reduction in the considered setting.

Citations

• Global Homotopies for Differential Hochschild Cohomologies
• Constraint Vector Bundles and Reduction of Lie (Bi-)Algebroids
• Convergent Star Products on Cotangent Bundles of Lie Groups
• Convergence of Star Product: From Examples to a General Framework
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• Kontsevich star-product on the dual of a Lie algebra
• Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications
• Homogeneous Fedosov star products on cotangent bundles II: GNS representations, the WKB expansion, traces, and applications
• On Riemann-Roch Formulas for Multiplicities

Related

• Variations on deformation quantization
• Infinitesimal Star Products Compatible with Coisotropic Reduction
• (Bi)modules, morphismes et réduction des star-produits: le cas symplectique, feuilletages et obstructions
• Closedness of star products and cohomologies
• Lie Algebra Quantization by the Star Product