# A homological approach to singular reduction in deformation quantization

@inproceedings{Bordemann2006AHA, title={A homological approach to singular reduction in deformation quantization}, author={Martin Bordemann and Hans-Christian Herbig and Markus J. Pflaum}, year={2006} }

We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are discussed, among others one where the singularity type is worse than an orbifold singularity.

## 18 Citations

Remarks on Singular Symplectic Reduction and Quantization of the Angular Moment

- Mathematics
- 2013

A direct algebraic method of symplectic reduction is demonstrated for some singular problems. The problem of quantization of singular surfaces is discussed. Mathematics Subject Classification (2010).…

Algebraic symplectic reduction and quantization of singular spaces

- Mathematics, Physics
- 2017

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular…

Remarks on Singular Symplectic Reduction and Quantization of the Angular Moment

- Mathematics
- 2013

A direct algebraic method of symplectic reduction is demonstrated for some singular problems. The problem of quantization of singular surfaces is discussed.

Quantization of Whitney functions and reduction

- Mathematics
- 2013

For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization…

Morita theory in deformation quantization

- Mathematics, Physics
- 2010

Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds are discussed. We relate the three flavours ring-theoretic Morita…

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

- Mathematics
- 2009

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443–461. World Scientific, Hackensack,…

Equivariant quantization of orbifolds

- Mathematics, Physics
- 2010

Abstract Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the…

Quantization of Whitney functions

- Mathematics
- 2012

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the…

Coisotropic Triples, Reduction and Classical Limit

- Mathematics
- 2019

Coisotropic reduction from Poisson geometry and deformation quantization is cast into a general and unifying algebraic framework: we introduce the notion of coisotropic triples of algebras for which…

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