# BRST Reduction of Quantum Algebras with $$^*$$-Involutions

@article{Esposito2019BRSTRO, title={BRST Reduction of Quantum Algebras with \$\$^*\$\$-Involutions}, author={Chiara Esposito and Andreas Kraft and Stefan Waldmann}, journal={Communications in Mathematical Physics}, year={2019} }

In this paper we investigate the compatibility of the BRST reduction procedure with the Hermiticity of star products. First, we introduce the generalized notion of abstract BRST algebras with corresponding involutions. In this setting we define adjoint BRST differentials and as a consequence one gets new BRST quotients. Passing to the quantum BRST setting we show that for compact Lie groups the new quantum BRST quotient and the quantum BRST cohomology are isomorphic in zero degree implying that…

## 4 Citations

### Deformation Quantization and Homological Reduction of a Lattice Gauge Model

- MathematicsCommunications in Mathematical Physics
- 2021

For a compact Lie group G we consider a lattice gauge model given by the G -Hamiltonian system which consists of the cotangent bundle of a power of G with its canonical symplectic structure and…

### The strong homotopy structure of Poisson reduction

- MathematicsJournal of Noncommutative Geometry
- 2022

In this paper we propose a reduction scheme for multivector fields phrased in terms of $L_\infty$-morphisms. Using well-know geometric properties of the reduced manifolds we perform a Taylor…

### The Strong Homotopy Structure of BRST Reduction

- Mathematics
- 2022

In this paper we propose a reduction scheme for polydifferential operators phrased in terms of L∞-morphisms. The desired reduction L∞-morphism has been obtained by applying an explicit version of the…

### Deformation Quantization and Homological Reduction of a Lattice Gauge Model

- MathematicsCommunications in Mathematical Physics
- 2021

For a compact Lie group G we consider a lattice gauge model given by the G-Hamiltonian system which consists of the cotangent bundle of a power of G with its canonical symplectic structure and…

## References

SHOWING 1-10 OF 45 REFERENCES

### Characteristic classes of star products on Marsden–Weinstein reduced symplectic manifolds

- Mathematics
- 2017

In this note we consider a quantum reduction scheme in deformation quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann based on BRST cohomology. We explicitly construct…

### BRST Cohomology and Phase Space Reduction in Deformation Quantization

- Mathematics
- 1999

Abstract:In this article we consider quantum phase space reduction when zero is a regular value of the momentum map. By analogy with the classical case we define the BRST cohomology in the framework…

### On Positive Deformations of ∗ -Algebras ∗

- Mathematics
- 2000

Motivated by deformation quantization we consider *-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the *-involution and discuss a…

### Completely positive inner products and strong morita equivalence

- Mathematics
- 2003

We develop a general framework for the study of strong Morita equivalence in which C*-algebras and hermitian star products on Poisson manifolds are treated in equal footing. We compare strong and…

### A proof of Tsygan's formality conjecture for Hamiltonian actions

- Mathematics
- 2018

In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant…

### Classification of Equivariant Star Products on Symplectic Manifolds

- Mathematics
- 2016

In this note, we classify invariant star products with quantum momentum maps on symplectic manifolds by means of an equivariant characteristic class taking values in the equivariant cohomology. We…

### Fedosov *-Products and Quantum Momentum Maps

- Mathematics, Physics
- 1996

Abstract:The purpose of this paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps” we give…