Infinitesimal Star Products Compatible with Coisotropic Reduction
Marvin Dippell
TL;DR
This paper characterizes infinitesimal star products on Poisson manifolds that are compatible with coisotropic reduction, using Hochschild cohomology of the constraint algebra.
Contribution
It introduces a method to compute the second constraint Hochschild cohomology for submanifolds with simple distributions, advancing the understanding of compatible star products.
Findings
Computed the second constraint Hochschild cohomology for constraint algebras.
Identified conditions for infinitesimal star products to be compatible with coisotropic reduction.
Provided a framework applicable to any submanifold with a simple distribution.
Abstract
We determine infinitesimal star products on Poisson manifolds compatible with coisotropic reduction. This is achieved by computing the second constraint Hochschild cohomology of the constraint algebra of functions associated to any submanifold equipped with a simple distribution.
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Taxonomy
TopicsMathematics and Applications